Question

2 (x + 2y = -14)
(-2x - 6y = 40)

2x + 4y = -28
-2x - 6y = 40
\overline{0x - 2y = 12}

solve for y:
-2y = 12
y = -6

plug in y = -6 into either equation and solve for x
x + 2y = -14 or -2x - 6y = 40

x = \square

Explanation:

Step1: Substitute \( y = -6 \) into \( x + 2y = -14 \)

We know \( y = -6 \), so substitute it into the equation \( x + 2y = -14 \). The equation becomes \( x + 2\times(-6) = -14 \).

Step2: Simplify and solve for \( x \)

First, calculate \( 2\times(-6) = -12 \). So the equation is \( x - 12 = -14 \). Then, add 12 to both sides of the equation: \( x = -14 + 12 \). Calculating the right side, we get \( x = -2 \). We can also check with the other equation \( -2x - 6y = 40 \). Substitute \( y = -6 \) and \( x = -2 \): \( -2\times(-2) - 6\times(-6) = 4 + 36 = 40 \), which matches the equation. So \( x = -2 \).

Answer:

\( -2 \)