Question

Solve the system of equations.

\[\begin{aligned}
&-5x+4y = 3\\\\
&x=2y-15
\end{aligned}\]
\[ x=\]
\[y=\]

Answer 1

To solve the system of equations

\[
\begin{aligned}
&-5x + 4y = 3 \quad (1) \\
&x = 2y - 15 \quad (2)
\end{aligned}
\]

we can substitute equation (2) into equation (1).

Substituting \(x\) from (2) into (1):

\[
-5(2y - 15) + 4y = 3
\]

Now, we simplify this equation:

\[
-10y + 75 + 4y = 3
\]

Combine like terms:

\[
-10y + 4y + 75 = 3
\]

This simplifies to:

\[
-6y + 75 = 3
\]

Now, isolate \(y\):

\[
-6y = 3 - 75
\]

\[
-6y = -72
\]

Now divide both sides by -6:

\[
y = \frac{-72}{-6} = 12
\]

Now that we have \(y\), we can find \(x\) by substituting \(y\) back into equation (2):

\[
x = 2(12) - 15
\]

\[
x = 24 - 15 = 9
\]

Thus, the solution to the system of equations is:

\[
\begin{aligned}
x &= 9 \\
y &= 12
\end{aligned}
\]

Final answer:

\[
x = 9, \quad y = 12
\]