Question

find the solution of the system of equations.\

$$\begin{cases}2x - 2y = -6\\\\4x - 2y = -12\\end{cases}$$

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

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases}2x - 2y = -6 \\ 4x - 2y = -12\end{cases}$$

Subtract the first equation from the second equation:
$$(4x - 2y) - (2x - 2y) = -12 - (-6)$$
Simplify the left side: \(4x - 2y - 2x + 2y = 2x\)
Simplify the right side: \(-12 + 6 = -6\)
So we get \(2x = -6\)

Step2: Solve for x

Divide both sides of \(2x = -6\) by 2:
\(x = \frac{-6}{2} = -3\)

Step3: Substitute x into first equation

Substitute \(x = -3\) into \(2x - 2y = -6\):
\(2(-3) - 2y = -6\)
Simplify: \(-6 - 2y = -6\)

Step4: Solve for y

Add 6 to both sides: \(-2y = -6 + 6 = 0\)
Divide both sides by -2: \(y = \frac{0}{-2} = 0\)

Answer:

\(x = -3\), \(y = 0\)