9. Q9a
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Similar Question 1
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle x+3 y=2\\2 x+5 y=3 </code></p>
Similar Question 2
<p>Find the exact solution to the linear system.</p><p><code class='latex inline'>\displaystyle x+3 y=0\\3 x-6 y=5 </code></p>
Similar Question 3
<p>What is the solution to the following linear system?</p><p><code class='latex inline'>\begin{array}{c} y=3x-22 \\ y=4x-29 \end{array}</code></p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle 3 f=g-4\\2 g=f+3 </code></p>
<p>Decide which variable to isolate. Then substitute for this variable, and solve the system. </p><p><code class='latex inline'> \displaystyle 3x - 2y = 10, x + 3y = 7 </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle a+4 b=3\\5 b=-2 a+3 </code></p>
<p>Solve by substitution. Check your answers.</p><p><code class='latex inline'>\displaystyle x -2y =5 </code></p><p><code class='latex inline'>\displaystyle 2x + 3y = 17 </code></p>
<p>Find the exact solution to the linear system.</p><p><code class='latex inline'>\displaystyle 4 x+y=0\\x+2 y+1=0 </code></p>
<p>Solve the linear system.</p><p><code class='latex inline'>\displaystyle 2 x-y=5 </code></p><p><code class='latex inline'>\displaystyle 3 x+y=-9 </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle 3 a+4 b=15\\a+b=5 </code></p>
<p> Solve each system.</p><p><code class='latex inline'>6x - 2y + 1 = 0</code> and <code class='latex inline'>3x - 5y + 7 = 0</code></p>
<p>Use the substitution method to solve each linear system.</p><p><code class='latex inline'>\displaystyle x+4 y=5 </code></p><p><code class='latex inline'>\displaystyle x+2 y=7 </code></p>
<p>Find the point of intersection of each pair of lines.</p><p><code class='latex inline'> \displaystyle \begin{cases} 2x = y + 5 \to \text{ eq1}\\ 3x + y = -9 \to \text{ eq2} \end{cases} </code></p>
<p>Decide which variable to isolate. Then substitute for this variable, and solve the system. </p><p><code class='latex inline'> \displaystyle 2x + y =5, x - 3y = 13 </code></p>
<p>Find the point of intersection of each pair of lines.</p><p><code class='latex inline'> \displaystyle \begin{cases} p + 4q = 3 \to \text{ eq1}\\ 5p = -2q + 3 \to \text{ eq2} \end{cases} </code></p>
<p>Find the exact solution to the linear system.</p><p><code class='latex inline'>\displaystyle 3 e-f-2=0\\5 e+2 f=3 </code></p>
<p> Solve for <code class='latex inline'>x</code> and <code class='latex inline'>y</code> using the substitution method for each linear system.</p> <ul> <li><code class='latex inline'>\displaystyle 3x = 5 + 2y</code></li> <li> <code class='latex inline'>2x - 2y = 7</code></li> </ul>
<p>Find the point of intersection for each pair of lines. Check your answers.</p><p><code class='latex inline'> 5x=y+11</code></p><p><code class='latex inline'>2x+y=3</code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle 2 x+3 y=5\\x-4 y=-14 </code></p>
<p>Solve the linear system using the method of substitution. Check the solution.</p><p><code class='latex inline'>\begin{array}{c} a+b=5 \\ 3a+4b=15 \end{array}</code></p>
<p>Use substitution to solve each system.</p><p><code class='latex inline'> \displaystyle \begin{array}{lllll} & 2x + 3y = 7 \\ & -2x - 1 = y \\ \end{array} </code></p>
<p>Find the exact solution to the linear system.</p><p><code class='latex inline'>\displaystyle 2 x-5 y=12\\x+10 y=-9 </code></p>
<p>Decide which variable to isolate in one of the equations in each system. Then substitute for this variable in the other equation, and solve the system.</p><p><code class='latex inline'> \displaystyle \begin{array}{llll} 2x + y = 4 \\ 3x - 16y = 6 \\ \end{array} </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle 6 x=3 y+2\\y-2 x+4=0 </code></p>
<p>Decide which variable to isolate. Then substitute for this variable, and solve the system. </p><p><code class='latex inline'> \displaystyle 3x - 2y = 10, x + 3y = 7 </code></p>
<p>Find the exact solution to the linear system.</p><p><code class='latex inline'>\displaystyle 3 a-2 b=-12\\a-4 b=8 </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle x+y-4=0\\2 x=8-2 y </code></p>
<p>Solve the linear system.</p><p><code class='latex inline'>\displaystyle 8 x-y=10 </code></p><p><code class='latex inline'>\displaystyle 3 x-y=9 </code></p>
<p> Solve each system.</p><p><code class='latex inline'>3 = 2a - b</code> and <code class='latex inline'>4a - 3b = 5</code></p>
<p>Use the substitution method to solve each linear system.</p><p><code class='latex inline'>\displaystyle x-3 y=-2 </code></p><p><code class='latex inline'>\displaystyle 2 x+5 y=7 </code></p>
<p>What is the solution to the following linear system?</p><p><code class='latex inline'>\begin{array}{c} y=3x-22 \\ y=4x-29 \end{array}</code></p>
<p>Is <code class='latex inline'>(3, -5)</code> the solution for the following linear system? Explain how you can tell.</p><p><code class='latex inline'> \displaystyle \begin{cases} 2x + 5y = -19 \text{ eq1}\\ 6y - 8x = 54 \text{ eq2} \end{cases} </code></p>
<p> Solve each system.</p><p><code class='latex inline'>6x - 2y + 1 = 0</code> and <code class='latex inline'>3x - 5y + 7 = 0</code></p>
<p> Use substitution to solve the linear system <code class='latex inline'>4x + y = 1</code> and <code class='latex inline'>x - 2y = -11</code>. </p>
<p>In each pair, decide which equation you will use first to solve for one variable in terms of the other variable. Do that step. Do not solve the linear system.</p><p><code class='latex inline'> \displaystyle \begin{cases} x + 2y = 5\\ 3x + 2y = 6 \end{cases} </code></p>
<p> Solve each system.</p><p> <code class='latex inline'>3c + 2d = -24</code> and <code class='latex inline'>2c + 5d = -38</code></p>
<p>Use substitution to solve each system.</p><p><code class='latex inline'> \displaystyle \begin{array}{lllll} & 5x + 2y = 18 \\ & 2x + 3y = 16 \\ \end{array} </code></p>
<p>Decide which variable to isolate in one of the equations in each system. Then substitute for this variable in the other equation, and solve the system.</p><p><code class='latex inline'> \displaystyle \begin{array}{llll} 2x + y = 4 \\ 3x - 16y = 6 \\ \end{array} </code></p>
<p>Is <code class='latex inline'>(4, -3)</code> the solution for the following linear system? Explain how you can tell.</p><p><code class='latex inline'>\displaystyle 2x - 2y = 18 </code></p><p><code class='latex inline'>\displaystyle 2x + 3y =- 1 </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle 2 x-y=13\\x+2 y=-6 </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle x+3 y=2\\2 x+5 y=3 </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle 2 r-s=2\\3 r-2 s=3 </code></p>
<p>Solve the linear system.</p><p><code class='latex inline'>\displaystyle 6x+3 y=5 </code></p><p><code class='latex inline'>\displaystyle x-2 y=0 </code></p>
<p>Use the substitution method to solve each linear system.</p><p><code class='latex inline'>\displaystyle x-3 y=5 </code></p><p><code class='latex inline'>\displaystyle 7 x+2 y=12 </code></p>
<p>Decide which variable to isolate. Then substitute for this variable, and solve the system. </p><p> <code class='latex inline'> \displaystyle x + 2y =0, x -y = -4 </code></p>
<p>Find the point of intersection of each pair of lines by solving the system of linear equation below.</p><p><code class='latex inline'> \displaystyle \begin{cases} a+ b + 6 = 0 \to \text{ eq1}\\ 2a - b - 3 = 0 \to \text{ eq2} \end{cases} </code></p>
<p>Use the substitution method to solve each linear system.</p><p><code class='latex inline'>\displaystyle 3 x-y=4 </code></p><p><code class='latex inline'>\displaystyle x+y=8 </code></p>
<p>Use substitution to solve the system.</p><p> <code class='latex inline'> \displaystyle \begin{array}{lllll} & 9 = 6x - 3y \\ & 4x - 3y = 5 \\ \end{array} </code></p>
<p>Solve using the substitution method.</p><p><code class='latex inline'>\displaystyle x-y=9 </code></p><p><code class='latex inline'>\displaystyle x+y=3 </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle x-2 y=5\\2 x-3 y=6 </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle x-2 y=4\\2 x-3 y=7 </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle 3 x+y=-9\\5 x-3 y=-1 </code></p>
<p>Solve by substitution. Check your solution.</p><p><code class='latex inline'> \displaystyle \begin{cases} 3a + 2b = 4 \to \text{ eq1}\\ 2a + b = 6 \to \text{ eq2} \end{cases} </code></p>
<p> Solve for <code class='latex inline'>x</code> and <code class='latex inline'>y</code> using the substitution method for each linear system.</p> <ul> <li><code class='latex inline'>3x + y = 3</code></li> <li> <code class='latex inline'>5x - 2y = 1</code></li> </ul>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle 2 x+y=6\\3 x+2 y=10 </code></p>
<p>Find the point of intersection of each pair of lines.</p><p><code class='latex inline'> \displaystyle \begin{cases} 4x + 2y = 7 \text{ eq1}\\ -x -y = 6 \text{ eq2} \end{cases} </code></p>
<p>Solve by substitution. Check your solution.</p><p><code class='latex inline'> \displaystyle \begin{cases} 6x + 5y = 7 \to \text{ eq1}\\ x - y = 3 \to \text{ eq2} \end{cases} </code></p>
<p>In each pair, decide which equation you will use first to solve for one variable in terms of the other variable. Do that step. Do not solve the linear system.</p><p><code class='latex inline'> \displaystyle \begin{cases} 2x + 5y = 7 \to \text{ eq1 }\\ x - 3y = -2 \to \text{ eq2 } \end{cases} </code></p>
<p>Use the substitution method to solve each linear system.</p><p><code class='latex inline'>\displaystyle 2 x+y=3 </code></p><p><code class='latex inline'>\displaystyle 4 x-3 y=1 </code></p>
<p>Solve the equation.</p><p><code class='latex inline'>\displaystyle x - 4y = 8 </code></p><p><code class='latex inline'>\displaystyle 2x - 8y = 8 </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle 5=2 y-x\\7=3 y-2 x </code></p>
<p>Find the point of intersection of each pair of lines.</p><p><code class='latex inline'> \displaystyle \begin{cases} x - 2y -2 = 0 \to \text{ eq1}\\ 3x + 4y - 16 = 0 \to \text{ eq2} \end{cases} </code></p>
<p>Explain why the following linear system is not easy to solve by substitution.</p><p><code class='latex inline'> \displaystyle \begin{array}{ccccc} & 3x + 4y = 10 \\ & 2x - 5y = 9 \end{array} </code></p>
<p>Solve using the substitution method.</p><p><code class='latex inline'>\displaystyle 2 x+y=2 </code></p><p><code class='latex inline'>\displaystyle 3 x+2 y=5 </code></p>
<p>Solve by substitution. Check your answers.</p><p><code class='latex inline'>\displaystyle x + 3y = 5 </code></p><p><code class='latex inline'>\displaystyle 4x + 2y = 10 </code></p>
<p>Find the exact solution to the linear system.</p><p><code class='latex inline'>\displaystyle x+7 y=1\\3 x-14 y=-7 </code></p>
<p>Solve by substitution. Check your solution.</p><p><code class='latex inline'> \displaystyle \begin{cases} x + 2y = 3 \to \text{ eq1}\\ 5x + 4y = 8 \to \text{ eq2} \end{cases} </code></p>
<p>Solve by substitution. Check your answers.</p><p><code class='latex inline'>\displaystyle 5a + b = 4 </code></p><p><code class='latex inline'>\displaystyle 3a +2 b = - 6 </code></p>
<p>Use the substitution method to solve each linear system.</p><p><code class='latex inline'>\displaystyle 2x+3 y=-1 </code></p><p><code class='latex inline'>\displaystyle x+y=1 </code></p>
<p>Use the substitution method to solve each linear system.</p><p><code class='latex inline'>\displaystyle 6 x+5 y=7 </code></p><p><code class='latex inline'>\displaystyle x-y=3 </code></p>
<p>Solve using the substitution method.</p><p><code class='latex inline'>\displaystyle 2 x-3 y=6 </code></p><p><code class='latex inline'>\displaystyle 2 x-y=7 </code></p>
<p>Solve the linear system using the method of substitution. Check the solution.</p><p><code class='latex inline'>\begin{array}{c} x + 3y = 0 \\ 3x-6y=5 \end{array}</code></p>
<p>Decide which variable to isolate. Then substitute for this variable, and solve the system. </p><p> <code class='latex inline'> \displaystyle x + 2y =0, x -y = -4 </code></p>
<p>Decide which variable to isolate in one of the equations in each system. Then substitute for this variable in the other equation, and solve the system.</p><p> <code class='latex inline'> \displaystyle \begin{array}{llll} x + 3y = 5 \\ 2x - 3y = -17 \\ \end{array} </code></p>
<p>Decide which variable to isolate. Then substitute for this variable, and solve the system. </p><p><code class='latex inline'> \displaystyle 2x + y =5, x - 3y = 13 </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle 2 c-d+2=0\\3 c+2 d+10=0 </code></p>
<p>Solve linear system using the method of substitution. Check your answers.</p><p><code class='latex inline'> \displaystyle \begin{cases} y = -2x + 3\\ 4x - 3y = -1 \end{cases} </code></p>
<p>Solve the linear system.</p><p><code class='latex inline'>\displaystyle 4 x+2 y=7 </code></p><p><code class='latex inline'>\displaystyle -x-y=6 </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle 2 x+3 y=6\\x+y=3 </code></p>
<p>Use substitution to solve the system.</p><p> <code class='latex inline'> \displaystyle \begin{array}{lllll} & 3x - 4y = 5 \\ & x -y = 5 \\ \end{array} </code></p>
<p>Find the exact solution to the linear system.</p><p><code class='latex inline'>\displaystyle 2 m-n=-2\\6 m+7 n=-1 </code></p>
<p>Solve using the method of substitution.</p><p><code class='latex inline'>\displaystyle 2 x-3 y=6\\2 x-y=7 </code></p>
<p>Find the exact solution to the linear system.</p><p><code class='latex inline'>\displaystyle x+3 y=0\\3 x-6 y=5 </code></p>
<p>In each pair, decide which equation you will use first to solve for one variable in terms of the other variable. Do that step. Do not solve the linear system.</p><p><code class='latex inline'> \displaystyle \begin{cases} 2x + y = 6 \text{ eq1 }\\ 3x + 2y = 10\text{ eq2 } \end{cases} </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle m+n+6=0\\2 m-n-3=0 </code></p>
<p>Solve linear system using the method of substitution. Check your answers.</p><p><code class='latex inline'> \displaystyle \begin{cases} y = 3x - 4\\ x + y =8 \end{cases} </code></p>
<p><strong>(a)</strong> What happens when you try to solve the following system by substitution?</p><p><code class='latex inline'> \displaystyle \begin{array}{cccccc} &4x - 2y = 9 \\ &y = 2x + 1 \\ \end{array} </code></p><p><strong>(b)</strong> Solve by graphing and explain how this is related to the solution when solving by substitution.</p>
<p>Find the point of intersection for each pair of lines. Check your answers.</p><p><code class='latex inline'>m+3n=4</code></p><p><code class='latex inline'>4m +2n+4=0</code></p>
<p> Solve each system.</p><p> <code class='latex inline'>3c + 2d = -24</code> and <code class='latex inline'>2c + 5d = -38</code></p>
<p>Find the exact solution to the linear system.</p><p><code class='latex inline'>\displaystyle 4 x-y=3\\6 x-2 y=5 </code></p>
<p>Solve linear system using the method of substitution. Check your answers.</p><p><code class='latex inline'> \displaystyle \begin{cases} x = -4y + 5\\ x + 2y = 7 \end{cases} </code></p>
<p> Solve each system of equations by substitution. If there is exactly one solution, check the solution.</p><p><code class='latex inline'>\displaystyle x-y=1\\3 x+y=11 </code></p>
<p>In each pair, decide which equation you will use first to solve for one variable in terms of the other variable. Do that step. Do not solve the linear system.</p><p><code class='latex inline'> \displaystyle \begin{cases} 2x - y = 2 \to \text{ eq1}\\ 4x + y =16 \to \text{ eq2} \end{cases} </code></p>
<p>Solve using the substitution method.</p><p><code class='latex inline'>\displaystyle x+y=-2 </code></p><p><code class='latex inline'>\displaystyle x-y=6 </code></p>
<p> Solve each system.</p><p><code class='latex inline'>7m + 2n = 21</code> and <code class='latex inline'>10m + 4n = - 10</code></p>
<p>Solve the linear system using the method of substitution. Check the solution.</p><p><code class='latex inline'>\begin{array}{c} 3m-2n=-12 \\ m-4n=8 \end{array}</code></p>
<p> Solve for <code class='latex inline'>x</code> and <code class='latex inline'>y</code> using the substitution method for each linear system.</p> <ul> <li><code class='latex inline'>\displaystyle 3x + y = 3</code></li> <li> <code class='latex inline'>5x - 2y = 2</code></li> </ul>
<p>Solve by substitution. Check your solution.</p><p><code class='latex inline'> \displaystyle \begin{cases} 2m + n = 2 \to \text{ eq1}\\ 3m - 2n =3 \to \text{ eq2} \end{cases} </code></p>
<p>Solve by substitution. Check your answers.</p><p><code class='latex inline'> 2m-3n = -10</code></p><p><code class='latex inline'>4m+n = 1</code></p>
<p>Decide which variable to isolate in one of the equations in each system. Then substitute for this variable in the other equation, and solve the system.</p><p> <code class='latex inline'> \displaystyle \begin{array}{llll} x + 3y = 5 \\ 2x - 3y = -17 \\ \end{array} </code></p>
<p> Solve each system.</p><p><code class='latex inline'>x + 3y = 7</code> and <code class='latex inline'>3x - 2y = - 12</code></p>
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