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Solve the following systems of equations.

  1. «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi»y«/mi»«mo»=«/mo»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mn»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»y«/mi»«mo»=«/mo»«mo»-«/mo»«mn»5«/mn»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» <br> <br> <div id="atto_collapsible_1421005247" class="atto_collapsible"> <div class="card" id="atto_collapsible_1421005247_0"> <div class="card-header" id="atto_collapsible_1421005247_0_title"><a class="collapsed" data-toggle="collapse" data-target="#atto_collapsible_1421005247_0_content" aria-expanded="false" aria-controls="atto_collapsible_1421005247_0_content" role="button"> Solution</a></div> <div style="height: 0px;" id="atto_collapsible_1421005247_0_content" class="collapse" aria-labelledby="atto_collapsible_1421005247_0_title" data-parent="#atto_collapsible_1421005247"> <div class="card-body"> Look for similarities between the two equations. Both have \(1y \). By subtracting the second equation from the first equation, you can eliminate the \(y \) variable. Then, you can solve for \(x \). <br> <br> <div class="row"> <div class="col-md-3">\[\begin{align}
     \cancel {y} &= 3x + 6 \\
     -(\cancel {y} &= -5x - 3)  \\
    \hline {} \\
     0 &= 8x + 9 \\
     -9 &= 8x \\
     -\frac{9}{8} &= x \\
     \end{align}\]


The solution is not complete. Now, solve for \(y \). Choose one of the two equations, and then substitute the value of \(x \) into that equation, and solve for \(y \).

\(\begin{align}
 y &= 3x + 6 \\
 y &= 3\left( { -\frac{9}{8}} \right) + 6 \\
 y &= \frac{{21}}{8} \\
 \end{align}\)

The solution to this system is \(x = -\frac{9}{8}\) and \(y = \frac{21}{8} \).