13. Q13
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Similar Question 1
<p>Create a situation that can be represented by a system of linear equations that has the ordered pair (5, 12) as its solution.</p>
Similar Question 2
<p> Sketch a graph to represent a system of two equations with one solution, so that the two lines have</p><p>a) different <code class='latex inline'> x </code> -intercepts and different <code class='latex inline'> y </code> -intercepts</p>
Similar Question 3
<p>Find the point of intersection of the lines <code class='latex inline'>3x + 5y=7</code> and <code class='latex inline'>2x + 4y=6</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>Use a graphing calculator to find the point of intersection of each pair of lines. </p><p><code class='latex inline'>\displaystyle 2x +5y + 20 = 0 </code></p><p><code class='latex inline'>\displaystyle 5x - 3y + 15 = 0 </code></p>
<p>Find the point of intersection of the lines <code class='latex inline'>3x + 5y=7</code> and <code class='latex inline'>2x + 4y=6</code>.</p>
<p>If <code class='latex inline'>3m + 5 = 23</code> and <code class='latex inline'>2n - 7 = 21</code>, find the value of of <code class='latex inline'>3m + 2n</code>.</p>
<p>Determine the values of the constant terms, so that the solution to each system is as shown.</p><p><code class='latex inline'>\displaystyle x-6 y=?\\4 x+5 y=?\\(-2,3) </code></p>
<p>Find the point of intersection for the linear system <code class='latex inline'>3x + 5y=2</code> and <code class='latex inline'>x - 3y=10</code>.</p>
<p>The solution to a system of linear equations is <code class='latex inline'> (2,5) </code> . If each equation is multiplied by 3 to produce a new system, is the solution to the new system <code class='latex inline'> (2,5),(6,15) </code> , or another ordered pair? Explain.</p>
<p>Explain why the following linear system has no solution.</p><p><code class='latex inline'>\displaystyle y - 2x = 1 </code></p><p><code class='latex inline'>\displaystyle y = 2x + 3 </code></p>
<p>Justify each step.</p><p><code class='latex inline'>\frac{4-2d}{5}+3=9</code></p><p><code class='latex inline'>\frac{4-2d}{5}+3-3=9-3</code></p><p><code class='latex inline'>\frac{4-2d}{5}=6</code></p><p><code class='latex inline'>\frac{4-2d}{5}(5)=6(5)</code></p><p><code class='latex inline'>4-2d=30</code></p><p><code class='latex inline'>4-2d-4=30-4</code></p><p><code class='latex inline'>-2d=26</code></p><p><code class='latex inline'>\frac{-2d}{-2}=\frac{26}{-2}</code></p><p><code class='latex inline'>d=-13</code></p><p>a. ?</p><p>b. ?</p><p>c. ?</p><p>d. ?</p><p>e. ?</p><p>f. ?</p><p>g. ?</p><p>h. ?</p>
<p>OPEN-ENDED Write a system of linear equations in which <code class='latex inline'>\displaystyle (3,-5) </code> is a solution of Equation 1 but not a solution of Equation 2, and <code class='latex inline'>\displaystyle (-1,7) </code> is a solution of the system.</p>
<p>Find the intersection point.</p><p><code class='latex inline'>\displaystyle y= \frac{1}{2}x -4 </code></p><p><code class='latex inline'>\displaystyle y = 2x- 1 </code></p>
<p>Find the equation of the line that passes through the point of intersection of <code class='latex inline'>-2x + 4y=14</code> and <code class='latex inline'>5x - 3y=-14</code>, and that is perpendicular to <code class='latex inline'>4x - 6y + 12=0</code>.</p>
<p> Determine the values of the constant terms, so that the solution to each system is as shown.</p><p><code class='latex inline'>\displaystyle 2 x-5 y=?\\3 x+4 y=? \quad\\(3,2) </code></p>
<p>Solve each linear system using the method of substitution.</p><p><code class='latex inline'>\displaystyle x + 4y =6 </code></p><p><code class='latex inline'>\displaystyle 2x -3y =1 </code></p>
<p>If <code class='latex inline'> (0,3) </code> and <code class='latex inline'> (2,4) </code> are both solutions to a system of two linear equations, does the system have any other solutions? Explain.</p>
<p>Use the clues to find the value of E. Describe your strategy.</p><p><code class='latex inline'>\displaystyle \begin{array}{llllllll} &A \times B = 80\\ &A \times C = 200\\ &B \times D = 36\\ &D \times E = 18\\ &C = 100 \end{array} </code></p>
<p>Solve by elimination. Check each solution.</p><p><code class='latex inline'>\displaystyle 5a -2b = 5 </code></p><p><code class='latex inline'>\displaystyle 3a +2b = 19 </code></p>
<img src="/qimages/11024" /><p>Which is a solution to the linear system? </p><p>A <code class='latex inline'>\displaystyle (-1,3) </code></p><p>B <code class='latex inline'>\displaystyle (-4,0) </code></p><p>C <code class='latex inline'>\displaystyle (0,4) </code></p><p>D <code class='latex inline'>\displaystyle (3,-1) </code></p>
<p>Use a graphing calculator to find the point of intersection of each pair of lines. </p><p><code class='latex inline'>\displaystyle y = 7x </code></p><p><code class='latex inline'>\displaystyle 3y =5x -2 </code></p>
<p>Find the coordinates of the point of intersection of each linear system.</p><img src="/qimages/1213" />
<p>Find the intersection point.</p><p><code class='latex inline'>\displaystyle x -y =4 </code></p><p><code class='latex inline'>\displaystyle 3x + 2y =7 </code></p>
<p>Solve each linear system using the method of substitution.</p><p><code class='latex inline'>\displaystyle y = 6-3x </code></p><p><code class='latex inline'>\displaystyle y = 2x +1 </code></p>
<p>Solve each linear system. Verify each solution by substituting the coordinates of your solution into both equations.</p><p><code class='latex inline'>x - y=8</code> and <code class='latex inline'>x + 2y=2</code></p>
<p>Solve each linear system. Verify each solution by substituting the coordinates of your solution into both equations.</p><p><code class='latex inline'>y=-\displaystyle{\frac{1}{2}}x + \displaystyle{\frac{9}{2}}</code> and <code class='latex inline'>y=3x - 6</code></p>
<p>Use a graphing calculator to find the point of intersection of each pair of lines. </p><p><code class='latex inline'>\displaystyle y = x -5 </code></p><p><code class='latex inline'>\displaystyle x + 2y =10 </code></p>
<p>Create a situation that can be represented by a system of linear equations that has the ordered pair (5, 12) as its solution.</p>
<p>Solve by elimination. Check each solution.</p><p><code class='latex inline'>\displaystyle 2a +b = 5 </code></p><p><code class='latex inline'>\displaystyle a - 2b = 10 </code></p>
<p>Solve each linear system using the method of substitution.</p><p><code class='latex inline'>\displaystyle 5x - y = 4 </code></p><p><code class='latex inline'>\displaystyle 3x + y =4 </code></p>
<p>Solve each linear system. Verify each solution by substituting the coordinates of your solution into both equations.</p><p><code class='latex inline'>x + 2y=7</code> and <code class='latex inline'>y=4x - 10</code></p>
<p>HOW DO YOU SEE IT? The graphs of two linear equations are shown.</p><img src="/qimages/139820" /><p>a. At what point do the lines appear to intersect?</p><p>b. Could you solve a system of linear equations by substitution to check your answer in part (a)? Explain.</p>
<p>If <code class='latex inline'>3a+8b=12</code>, then what is the value of <code class='latex inline'>15a+40b</code>?</p><p><strong>(a)</strong> 36</p><p><strong>(b)</strong> 48</p><p><strong>(c)</strong> 60</p><p><strong>(d)</strong> 84</p><p><strong>(e)</strong> 180</p>
<p> Solve the linear system.</p><p><code class='latex inline'>\displaystyle \frac{x-2}{3} + \frac{y + 1}{5} =2 </code></p><p><code class='latex inline'>\displaystyle \frac{x + 2}{7} - \frac{y + 5}{3} = -2 </code></p>
<p>Solve by elimination. Check each solution.</p><p><code class='latex inline'>\displaystyle 4k + 3h =12 </code></p><p><code class='latex inline'>\displaystyle 4k -h =4 </code></p>
<p>Find the point of intersection of <code class='latex inline'>x + 5y=9</code> and <code class='latex inline'>5x + 3y=1</code>.</p>
<p>Solve by elimination. Check each solution.</p><p><code class='latex inline'>\displaystyle x + y = 55 </code></p><p><code class='latex inline'>\displaystyle 2x - y = -4 </code></p>
<p>Find the coordinates of the point of intersection of each linear system.</p><img src="/qimages/1214" />
<p> Sketch a graph to represent a system of two equations with one solution, so that the two lines have</p><p>a) different <code class='latex inline'> x </code> -intercepts and different <code class='latex inline'> y </code> -intercepts</p>
<p>Find the intersection point.</p><p><code class='latex inline'>\displaystyle x + y - 4= 0 </code></p><p><code class='latex inline'>\displaystyle 5x -y -8=0 </code></p>
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