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:

\((-4,2)\)