Question

Solve the following system of linear equations by substitution: 8x-y=-13 6x-3y=15

Answer 1

$\begin{cases} 8x-y=-13 \\ 6x-3y=15 \end{cases}\\ \\ \begin{cases} -y=-8x-13 \ \ *(-1) \\ 6x-3y=15 \end{cases}\\ \\\begin{cases} y= 8x+13 \\ 6x-3(8x+13)=15 \end{cases} \\ \\\begin{cases} y= 8x+13 \\ 6x-24x-39=15 \end{cases}$

$\begin{cases} y= 8x+13 \\ 6x-24x =15+39 \end{cases} \\ \\\begin{cases} y= 8x+13 \\ -18x =54 \ \ / :(-18)\end{cases} \\ \\\begin{cases} y= 8*(-3)+13 \\ x = -3 \end{cases} \\ \\\begin{cases} y= -24+13 \\ x = -3 \end{cases} \\ \\ \begin{cases} y= -11 \\ x = -3 \end{cases}$

Answer 2

Rearrange 8x-y=-13 to y=8x+13
Substitute this in so:
6x-3(8x+13)=15
6x-24x-39=15
-18x-39=15
-18x=54
x=-3

Substitute x into 1st equation:
Y=(8*-3)+13
Y=-24+13
Y=-11