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A system of equations is given below. What is the value of y in the (x,y) solution to the system? x = 4y- 13 x= y+2

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Starting with the system of equations:


\begin{gathered} x=4y-13 \\ x=y+2 \end{gathered}

Substitute the expression for x in the second equation into the first one:


y+2=4y-13

Solve for y:


\begin{gathered} \Rightarrow y+2-2=4y-13-2 \\ \Rightarrow y=4y-15 \\ \Rightarrow y-4y=4y-15-4y \\ \Rightarrow-3y=-15 \\ \Rightarrow y=(-15)/(-3) \\ \Rightarrow y=5 \end{gathered}

Therefore, y=5.

User Andrew Reid
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