Question

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

Explanation:

Step1: Define the system of equations

We have the system:

$$
LATEXBLOCK0
$$

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 \(2x - 2y = -18\):

$$
LATEXBLOCK1
$$

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:

\((-2, 7)\)