Question

1. what is the solution to the system of equations below?

-4y - 11x = 36
4 = -2x - 2y
( , )

Explanation:

Step1: Simplify the second equation

The second equation is \(4 = -2x - 2y\). We can divide both sides by \(-2\) to simplify it.
\[
\frac{4}{-2}=\frac{-2x - 2y}{-2}
\]
\[

• 2=x + y

\]
Then we can express \(y\) in terms of \(x\): \(y=-x - 2\).

Step2: Substitute \(y\) into the first equation

The first equation is \(-4y-11x = 36\). Substitute \(y=-x - 2\) into this equation:
\[
-4(-x - 2)-11x=36
\]
First, distribute \(-4\) in \(-4(-x - 2)\):
\[
4x + 8-11x=36
\]
Combine like terms:
\[
-7x+8 = 36
\]
Subtract \(8\) from both sides:
\[
-7x=36 - 8
\]
\[
-7x=28
\]
Divide both sides by \(-7\):
\[
x=\frac{28}{-7}=- 4
\]

Step3: Find the value of \(y\)

We know that \(y=-x - 2\), substitute \(x = - 4\) into this formula:
\[
y=-(-4)-2
\]
\[
y = 4-2=2
\]

Answer:

\((-4,2)\)