Question

Solve using substitution.

–5x + 4y = 5
–8x + 9y = –5

Answer 1

To solve the system of equations using substitution, we first solve one of the equations for one variable and then substitute that expression into the other equation. Let’s start with the first equation:

\[
-5x + 4y = 5
\]

We can solve for \( y \):

\[
4y = 5 + 5x
\]

\[
y = \frac{5 + 5x}{4}
\]

Now that we have \( y \) in terms of \( x \), we can substitute this expression for \( y \) into the second equation:

\[
-8x + 9y = -5
\]

Substituting \( y \):

\[
-8x + 9\left(\frac{5 + 5x}{4}\right) = -5
\]

To eliminate the fraction, multiply the entire equation by 4:

\[
-32x + 9(5 + 5x) = -20
\]

Distributing the 9:

\[
-32x + 45 + 45x = -20
\]

Combining like terms:

\[
13x + 45 = -20
\]

Now, isolate \( x \):

\[
13x = -20 - 45
\]
\[
13x = -65
\]
\[
x = -5
\]

Now that we have the value of \( x \), we can substitute it back into the expression we found for \( y \):

\[
y = \frac{5 + 5(-5)}{4}
\]
\[
y = \frac{5 - 25}{4}
\]
\[
y = \frac{-20}{4}
\]
\[
y = -5
\]

Thus, the solution to the system of equations is:

\[
\boxed{(-5, -5)}
\]