Question

x-y=-9. 8x-3y=-62. solve each system of equations by substitution clearly identify your solution

Answer 1

x= -7

y=2

Explanation

Step 1

Let

$\begin{gathered} x-y=-9\text{ Equation (1)} \\ 8x-3y=-62\text{ Equation (2)} \end{gathered}$

Step 2

isolate x form equation (1)

$\begin{gathered} x-y=-9 \\ x=-9+y \end{gathered}$

Step 3

replace the value of x in equation (2) to find y

$\begin{gathered} 8x-3y=-62 \\ \text{then} \\ 8(-9+y)-3y=-62 \\ -72+8y-3y=-62 \\ 5y=-62+72 \\ 5y=10 \\ y=\frac{10}{5} \\ y=2 \end{gathered}$

Hence, y=2

Step 4

Finally, replace the value of y = 2 in equation (1) to find x

$\begin{gathered} x-y=-9 \\ x-2=-9 \\ \text{add 2 in both sides} \\ x-2+2=-9+2 \\ x=-9+2 \\ x=-7 \end{gathered}$