Question

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

Answer 1

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:

$\begin{gathered} \Rightarrow y+2-2=4y-13-2 \\ \Rightarrow y=4y-15 \\ \Rightarrow y-4y=4y-15-4y \\ \Rightarrow-3y=-15 \\ \Rightarrow y=\frac{-15}{-3} \\ \Rightarrow y=5 \end{gathered}$

Therefore, y=5.