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Similar Question 1
<p>Which of the following system of equations is equivalent linear system to the graph shown below?</p><p>a) <code class='latex inline'>y = 2x + 1, 2x - 3y = 9</code></p><p>b) <code class='latex inline'>x = -3, y = -5</code></p><p>c) <code class='latex inline'>4x -2y + 2 = 0</code>, <code class='latex inline'>4x - 6y - 18 = 0</code></p><img src="/qimages/5165" />
Similar Question 2
<p>Can a system of two linear equations have exactly two solutions? Explain.</p>
Similar Question 3
<p>Solve the following systems of equations, and explain the nature of each intersection:</p><p><code class='latex inline'>\displaystyle \begin{array}{lllll} &7x -3y &= 9 \\ &35x - 15y &= 45 \end{array} </code></p>
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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>Which of the following pair are equivalent to below.</p><p><code class='latex inline'>y = \frac{3}{5}x + 2</code></p>
<p>Solve the equation and verify your solution.</p><p><code class='latex inline'> x - y = 2</code> and <code class='latex inline'>2x + 3y = 19</code></p>
<p> Consider this system of linear equations:<br> <code class='latex inline'>\displaystyle \begin{array}{cccc} &2x + y = 7\\ &8x + 4y = 28 \\ \end{array} </code> </p><p><strong>a)</strong> Can you create an equivalent system that contains only one variable? </p><p><strong>b)</strong> What does your result for part a) suggest about the solution to the original system? </p><p><strong>c)</strong> What does your result for part a) suggest about the graphs of both lines? </p>
<p>Add and subtract the equations in each linear system to create a new linear system.</p><p><code class='latex inline'> x - 3y = 2</code> and <code class='latex inline'>2x + y = -5</code></p>
<p>Which linear system below is equivalent to the system that is shown in the graph?</p><p><code class='latex inline'> \displaystyle \begin{array}{llllll} &\text{A}. &2x - 5y =4 &\text{B}. &x - 3y = -1\\ &&-x + y = 1 && 2x + y = 4 \\ \end{array} </code></p><img src="/qimages/3349" />
<p>The sum of two numbers is 33, and their difference is 57.</p><p><strong>a)</strong> Create a system of linear equations for this situation.</p><p><strong>b)</strong> Create an equivalent system by adding and subtracting your equations. </p><p><strong>c)</strong> Solve the equivalent system to determine the two numbers. </p>
<p>Which is not an equivalent linear relation?</p><p><strong>A</strong> <code class='latex inline'>8y = 12x +4</code></p><p><strong>B</strong> <code class='latex inline'>4y = 6x +2</code></p><p><strong>C</strong> <code class='latex inline'>2y = 3x + 4</code></p><p><strong>D</strong> <code class='latex inline'>y = \frac{3}{2}x + \frac{1}{2}</code></p>
<p>Solve the following systems of equations, and explain the nature of each intersection:</p><p><code class='latex inline'>\displaystyle \begin{array}{lllll} &2x + y &= 3 \\ &2x + y &= 4 \\ \end{array} </code></p>
<p>A linear system is shown on the graph.</p><img src="/qimages/698" /><p><code class='latex inline'>y = 2x </code> ---&gt;<strong>eqn 1</strong></p><p><code class='latex inline'>y = 6- x </code> ---&gt;<strong>eqn 2</strong></p><p><code class='latex inline'>2y = x + 6 </code>---&gt;<strong>eqn 3</strong></p><p><code class='latex inline'>0 = 3x - 6 </code>---&gt;<strong>eqn 4</strong></p><p>(b) How is equation <strong>eqn 3</strong> obtained from equations <strong>eqn 1</strong> and <strong>eqn 2</strong>?</p>
<p>For <code class='latex inline'>4x + y = 4, 2x - 3y = -5 </code></p> <ul> <li>Show that your solution also satisfies the equation <code class='latex inline'>2x + 11y = 23</code>. </li> </ul>
<p>Add and subtract the equations in each linear system to create a new linear system.</p><p><code class='latex inline'>4x + 2y = 8</code> and <code class='latex inline'>-x - 2y = -4</code></p>
<p> Consider this system of linear equations:<br> <code class='latex inline'>\displaystyle \begin{array}{cccc} & 2x + y = 7\\ &8x + 4y = 10\\ \end{array} </code> </p><p><strong>a)</strong> Can you create an equivalent system that contains only one variable? </p><p><strong>b)</strong> What does your result for part a) suggest about the solution to the original system? </p><p><strong>c)</strong> What does your result for part a) suggest about the graphs of both lines? </p>
<p>Which of the following pair are equivalent to below.</p><p><code class='latex inline'>3x + 6y = 12</code></p>
<p>Solve by elimination.</p><p><code class='latex inline'>\displaystyle \begin{array}{cccc} &2x + 3y = 4\\ &2x - 3y = 8 \end{array} </code></p>
<p> Solve each system.</p><p><code class='latex inline'>\displaystyle \frac{1}{4}x - 3y =\frac{1}{2}</code> and <code class='latex inline'>\displaystyle \frac{1}{3}x - 9y = 5</code></p>
<p> Solve each system.</p><p><code class='latex inline'>\displaystyle \frac{1}{4}x - 3y =\frac{1}{2}</code> and <code class='latex inline'>\displaystyle \frac{1}{3}x - 9y = 5</code></p>
<p>If the two spinners shown are each spun once, what is the probability that the sum of the two numbers is either even or a multiple of 3?</p><img src="/qimages/697" /><p><strong>A</strong> <code class='latex inline'>\dfrac{7}{13}</code></p><p><strong>B</strong> <code class='latex inline'>\dfrac{2}{3}</code></p><p><strong>C</strong> <code class='latex inline'>\dfrac{1}{3}</code></p><p><strong>D</strong> <code class='latex inline'>\dfrac{9}{13}</code></p><p><strong>E</strong> <code class='latex inline'>\dfrac{3}{4}</code></p>
<p>Which of the following pair are equivalent to below.</p><p><code class='latex inline'>8x + 4y = 10</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 \frac{2}{3}x + 2y = 4</code></li> <li> <code class='latex inline'>x + 3y = -2 </code></li> </ul>
<p>Add and subtract the equations in each linear system to create a new linear system.</p><p><code class='latex inline'> 3x + y = 3</code> and <code class='latex inline'>x - 2y = 8</code></p>
<p><strong>(a)</strong> State the solution to the linear system that is shown in the graph below.</p><img src="/qimages/700" /><p><strong>(b)</strong> Create a new linear system by adding and then subtracting the equations of the original system.</p>
<p>If <code class='latex inline'>\displaystyle \frac{p-q}{2} =3 </code> and <code class='latex inline'>rp -rq =12</code>, then <code class='latex inline'>r =</code></p><p>A) -1</p><p>B) 1</p><p>C) 2</p><p>D) 4</p><p>E) It cannot be determined from the given information</p>
<p>Which one of the following is equivalent linear system to below?</p><p><code class='latex inline'> \begin{array}{llll} &3x - 4y = 3\\ &-x -y = 6 \end{array} </code></p>
<p>A linear system is given.</p><p><code class='latex inline'>3x - 6y = 15 </code> <code class='latex inline'>\to</code> <strong>eqn 1</strong></p><p><code class='latex inline'>x + y = 3 </code> <code class='latex inline'>\to </code> <strong>eqn 2</strong></p><p>Explain why the following is an equivalent linear system.</p><p><code class='latex inline'>x - 2y = 5</code></p><p><code class='latex inline'>2x + 2y = 6</code></p>
<p>Which two equations are equivalent?</p><p><strong>A</strong> <code class='latex inline'>y = \frac{1}{2}x + 3</code></p><p><strong>B</strong> <code class='latex inline'>2y = x + 6</code></p><p><strong>C</strong> <code class='latex inline'>y = x+ 6</code></p>
<p>Which of the following pair are equivalent to below.</p><p><code class='latex inline'>y = 3x - 2</code></p><p>A. <code class='latex inline'>2y=6x-4;3y=9x-6</code></p><p>B. <code class='latex inline'>2y=6x-2;3y=9x-6</code></p><p>C. <code class='latex inline'>2y=6x-4;3y=5x-6</code></p><p>D. <code class='latex inline'>2y=6x-4;3y=9x+3</code></p>
<p>Can a system of two linear equations have exactly two solutions? Explain.</p>
<p> If you create equivalent linear systems in which there is only one variable in one or more of the new equations, you can solve the original system without graphing it. Use this strategy to solve the following linear systems. </p><p> <code class='latex inline'>\displaystyle \begin{array}{cccc} &3x - 4y = 30\\ &2x + 5y = -26\\ \end{array} </code> </p>
<p>Simplify and then solve each linear system.</p><p><code class='latex inline'>\displaystyle \begin{array}{lllll} 3c + 0.9d = 1.4\\ 0.5c -0.4d = 1.4 \end{array} </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>Solve each system by graphing. Check your solution.</p><p><code class='latex inline'>\displaystyle y=2 x </code></p><p><code class='latex inline'>\displaystyle y=-2 x+8 </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 0.1x + y = 3</code></li> <li> <code class='latex inline'>0.5x - 3y = 7</code></li> </ul>
<p>A linear system is shown on the graph.</p><p><code class='latex inline'>y = 2x </code> ---&gt; <strong>eqn 1</strong></p><p><code class='latex inline'>y = 6- x </code> ---&gt; <strong>eqn 2</strong></p><img src="/qimages/698" /> <ul> <li>Is the following system of equation equivalent to above set?</li> </ul> <p><code class='latex inline'>2y = x + 6 </code> ---&gt; <strong>eqn 3</strong></p><p><code class='latex inline'>0 = 3x - 6 </code> ---&gt; <strong>eqn 4</strong></p>
<ul> <li>Create another linear system by adding and subtracting the equations <code class='latex inline'>4x + y = 1</code> and <code class='latex inline'>x - 2y = -11</code>. </li> </ul>
<img src="/qimages/700" /><p>Determine the x- and y-intercepts of the new equation to verify that the graph of the new equation is the same as the graph of the original equation in the graph.</p>
<p>Solve this linear system: <code class='latex inline'>4x + y = 4, 2x - 3y = -5 </code></p>
<p>Solve the following systems of equations, and explain the nature of each intersection:</p><p><code class='latex inline'>\displaystyle \begin{array}{lllll} &7x -3y &= 9 \\ &35x - 15y &= 45 \end{array} </code></p>
<p>If you create equivalent linear systems in which there is only one variable in one or more of the new equations, you can solve the original system without graphing it. Use this strategy to solve the following linear systems. </p><p><code class='latex inline'>\displaystyle \begin{array}{cccc} & x - 4y = -22\\ & 2x + y = 1\\ \end{array} </code></p>
<p>The linear system <code class='latex inline'>6x + 5y= 10</code> and <code class='latex inline'>ax+ 2y = b</code> has an infinite number of solutions. Determine <code class='latex inline'>a</code> and <code class='latex inline'>b</code>.</p>
<p>Solve the equation and verify your solution.</p><p><code class='latex inline'> x - 3y = 2</code> and <code class='latex inline'>2x + y = -5</code></p>
<p>A linear system is shown on the graph.</p><img src="/qimages/698" /><p><code class='latex inline'>y = 2x </code> ---&gt;<strong>eqn 1</strong></p><p><code class='latex inline'>y = 6- x </code> ---&gt;<strong>eqn 2</strong></p><p><code class='latex inline'>2y = x + 6 </code> ---&gt;<strong>eqn 3</strong></p><p><code class='latex inline'>0 = 3x - 6 </code>---&gt;<strong>eqn 4</strong></p><p>How is equation <strong>eqn 4</strong> obtained from equations <strong>eqn 1</strong> and <strong>eqn 2</strong>?</p>
<p>Solve by elimination.</p><p><code class='latex inline'>\displaystyle \begin{array}{llllll} &2x + 3y = 4\\ &2x - 3y = 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 \frac{x}{2} + 3y = 4</code></li> <li> <code class='latex inline'>x + 3y = 9</code></li> </ul>
<p>Which of the following system of equations is equivalent linear system to the graph shown below?</p><p>a) <code class='latex inline'>y = 2x + 1, 2x - 3y = 9</code></p><p>b) <code class='latex inline'>x = -3, y = -5</code></p><p>c) <code class='latex inline'>4x -2y + 2 = 0</code>, <code class='latex inline'>4x - 6y - 18 = 0</code></p><img src="/qimages/5165" />
<p>Add and subtract the equations in each linear system to create a new linear system.</p><p><code class='latex inline'> x - y = 2</code> and <code class='latex inline'>2x + 3y = 19</code></p>
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