Question

Solve using substitution.

8x − 3y = –8
10x − 7y = 16

Answer 1

To solve the system of equations using substitution, we first need to solve one of the equations for one variable and then substitute it into the other equation.

Let's solve the first equation for \( y \):

Given the first equation:
\[
8x - 3y = -8
\]

Rearranging to isolate \( y \):
\[
-3y = -8 - 8x
\]
\[
3y = 8 + 8x
\]
\[
y = \frac{8 + 8x}{3}
\]

Now, we'll substitute this expression for \( y \) into the second equation:
\[
10x - 7y = 16
\]

Substituting \( y \):
\[
10x - 7\left(\frac{8 + 8x}{3}\right) = 16
\]

Multiply through by 3 to eliminate the fraction:
\[
30x - 7(8 + 8x) = 48
\]
\[
30x - 56 - 56x = 48
\]

Combine like terms:
\[
30x - 56x - 56 = 48
\]
\[
-26x - 56 = 48
\]

Add 56 to both sides:
\[
-26x = 104
\]

Now, divide by -26:
\[
x = -\frac{104}{26} = -4
\]

Now that we have \( x = -4 \), we can substitute this value back into the expression we found for \( y \):
\[
y = \frac{8 + 8(-4)}{3}
\]
\[
y = \frac{8 - 32}{3}
\]
\[
y = \frac{-24}{3} = -8
\]

So, the solution to the system of equations is:
\[
\boxed{(-4, -8)}
\]