Question

15 -3x - 3y = -6 -2x - 5y = -28

Explanation:

Step1: Simplify the first equation

Divide the first equation \(-3x - 3y = -6\) by \(-3\) to simplify it.
\[

$$\begin{align*} \frac{-3x - 3y}{-3}&=\frac{-6}{-3}\\ x + y&= 2\\ x&= 2 - y \end{align*}$$

\]

Step2: Substitute \(x = 2 - y\) into the second equation

Substitute \(x = 2 - y\) into \(-2x - 5y = -28\).
\[

$$\begin{align*} -2(2 - y) - 5y&= -28\\ -4 + 2y - 5y&= -28\\ -4 - 3y&= -28 \end{align*}$$

\]

Step3: Solve for \(y\)

Add \(4\) to both sides of the equation \(-4 - 3y = -28\).
\[

$$\begin{align*} -4 - 3y + 4&= -28 + 4\\ -3y&= -24 \end{align*}$$

\]
Divide both sides by \(-3\):
\[
y = \frac{-24}{-3} = 8
\]

Step4: Solve for \(x\)

Substitute \(y = 8\) into \(x = 2 - y\).
\[
x = 2 - 8 = -6
\]

Answer:

The solution to the system of equations is \(x = -6\) and \(y = 8\).