Question

Use substitution to find the solution to the system ofequation.-4x + y = 6-5x – y = 21

Answer 1

Let:

$\begin{gathered} -4x+y=6_{\text{ }}(1) \\ -5x-y=21_{\text{ }}(2) \end{gathered}$

From (1), solve for y:

$y=6+4x_{\text{ }}(3)$

Replace (3) into (2):

$\begin{gathered} -5x-(6+4x)=21 \\ -5x-6-4x=21 \\ -9x-6=21 \\ -9x=21+6 \\ -9x=27 \\ x=\frac{27}{-9} \\ x=-3 \end{gathered}$

Replace the value of x into (3):

$\begin{gathered} y=6+4(-3) \\ y=6-12 \\ y=-6 \end{gathered}$