Question

find the solution of the system of equations.\

$$\begin{cases}2x + 4y = -26\\\\2x - 2y = -2\\end{cases}$$

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show your work here\
x = \
y = \
check

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases} 2x + 4y = -26 \\ 2x - 2y = -2 \end{cases}$$

Subtract the second equation from the first equation:
$$(2x + 4y) - (2x - 2y) = -26 - (-2)$$
Simplify the left side: $2x + 4y - 2x + 2y = 6y$
Simplify the right side: $-26 + 2 = -24$
So we get $6y = -24$

Step2: Solve for y

Divide both sides of $6y = -24$ by 6:
$$y = \frac{-24}{6} = -4$$

Step3: Substitute y into one equation to find x

Substitute $y = -4$ into the second equation $2x - 2y = -2$:
$$2x - 2(-4) = -2$$
Simplify: $2x + 8 = -2$
Subtract 8 from both sides: $2x = -2 - 8 = -10$
Divide both sides by 2: $x = \frac{-10}{2} = -5$

Answer:

$x = -5$, $y = -4$