<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-elimination-method">Elimination Method Exercise</a></p><p>In the <span style="color:#27ae60;">Elimination Method</span>, you manipulate one or both of the equations so that, when you add one equation to the other or subtract one equation from the other, one of the variables is eliminated, allowing you to solve the system of equations.</p>
<p style="margin-left: 40px;"><span style="color:#e74c3c;">Example 1 (adding the equations to eliminate a variable)</span></p>
<p>$$3x+2y=7$$</p>
<p>$$5x-y=9.5$$</p>
<p style="text-align: center;">Multiply both sides of the second equation by $2$ to get the following:$10x-2y=19$. The equations now look this:</p>
<p>$$3x+2y=7$$</p>
<p>$$10x-2y=19$$</p>
<p style="text-align: center;">If you add the two equations together, you get $13x=26$, which means $x=2$. If $x=2$, $y$ must equal $0.5$.</p>
<p style="margin-left: 40px;"><span style="color:#e74c3c;">Example 2 (subtract the second equation from the first to eliminate a variable)</span></p>
<p>$$4x+5y=11$$</p>
<p>$$x+y=5$$</p>
<p style="text-align: center;">Multiply both sides of the second equation by $4$ to get the following: $4x+4y=20$. The equations now look like this:</p>
<p>$$4x+5y=11$$</p>
<p>$$4x+4y=20$$</p>
<p style="text-align: center;">If you subtract the second equation from the first, you get $y=-9$. If $y=-9$, $x$ must equal $14$.</p>