Question

Solve using substitution.
-9x + 6y = 15
x - 5y = -19
(_,_)

Answer 1

To solve the system of equations using substitution, we start with the two equations:

1) \(-9x + 6y = 15\)
2) \(x - 5y = -19\)

Let's solve the second equation for \(x\):

\[
x = 5y - 19
\]

Now that we have \(x\) expressed in terms of \(y\), we substitute it into the first equation:

\[
-9(5y - 19) + 6y = 15
\]

Distributing \(-9\):

\[
-45y + 171 + 6y = 15
\]

Combine like terms:

\[
-39y + 171 = 15
\]

Now, let's isolate \(y\) by subtracting 171 from both sides:

\[
-39y = 15 - 171
\]

\[
-39y = -156
\]

Now, divide both sides by -39:

\[
y = \frac{-156}{-39} = 4
\]

Now we have the value of \(y\). Next, we substitute \(y\) back into the expression we found for \(x\):

\[
x = 5(4) - 19
\]

\[
x = 20 - 19 = 1
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (1, 4)
\]

The final answer is:

\[
\boxed{(1, 4)}
\]