Question

-4x + y = 15; 2x - 2y = -18; ( , )

Explanation:

Step1: Define the system of equations

We have the system:
\[

$$\begin{cases} -4x + y = 15 \\ 2x - 2y = -18 \end{cases}$$

\]

Step2: Solve the first equation for \(y\)

From \(-4x + y = 15\), we can express \(y\) as \(y = 4x + 15\).

Step3: Substitute \(y\) into the second equation

Substitute \(y = 4x + 15\) into \(2x - 2y = -18\):
\[

$$\begin{align*} 2x - 2(4x + 15) &= -18 \\ 2x - 8x - 30 &= -18 \\ -6x - 30 &= -18 \end{align*}$$

\]

Step4: Solve for \(x\)

Add 30 to both sides:
\[
-6x = -18 + 30 = 12
\]
Divide both sides by \(-6\):
\[
x = \frac{12}{-6} = -2
\]

Step5: Substitute \(x\) back to find \(y\)

Substitute \(x = -2\) into \(y = 4x + 15\):
\[
y = 4(-2) + 15 = -8 + 15 = 7
\]

Answer:

\((-2, 7)\)