Test 4 Section 3 Number 19

This one is a great opportunity to practice solving a system of linear equations by elimination. Here are the equations you’re given:

    \begin{align*}-3x+4y&=20\\6x+3y&=15\end{align*}

Multiply both sides of the first equation by 2:

    \begin{align*}-6x+8y&=40\end{align*}

Now add that to the original second equation and you’re left with only y terms!

    \begin{align*}-6x+8y&=40\\+(6x+3y&=15)\\11y&=55\end{align*}

From that, you know that y = 5. The question asked you for x, though, so plug in 5 for y in one of the original equations to finish up:

    \begin{align*}6x+3(5)&=15\\6x+15&=15\\6x&=0\\x&=0\end{align*}

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