Question

what is the value of y in this system of equations?

\\(-6x + 2y = -18\\)
\\(-3x - 2y = 54\\)

Explanation:

Identify the system of equations

We are given a System of Equations with two linear equations:

$$
LATEXBLOCK0
$$

Our goal is to find the value of \(y\).

Eliminate the variable y to find x

Using the Linear Combination Method, we can add the two equations together because the coefficients of \(y\) are opposites (\(2\) and \(-2\)):

$$ (-6x + 2y) + (-3x - 2y) = -18 + 54 $$

$$ -9x = 36 $$

$$ x = -4 $$

Substitute x to solve for y

Now, substitute \(x = -4\) back into Equation 1 to solve for \(y\):

$$ -6(-4) + 2y = -18 $$

$$ 24 + 2y = -18 $$

Isolate the variable y

Subtract \(24\) from both sides of the equation:

$$ 2y = -18 - 24 $$

$$ 2y = -42 $$

Divide by \(2\):

$$ y = -21 $$

Answer:

What is the value of y in this system of equations? <blank>-21</blank>