Question

solve the system by the substitution method.

x + y = -2

y = -2x

Explanation:

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

We know that \( y = -2x \), so we can replace \( y \) in the first equation \( x + y = -2 \) with \( -2x \). This gives us the equation \( x + (-2x) = -2 \).

Step2: Simplify and solve for \( x \)

Simplify \( x + (-2x) \) to get \( -x \). So the equation becomes \( -x = -2 \). Multiply both sides by -1 to solve for \( x \), we get \( x = 2 \).

Step3: Substitute \( x = 2 \) into \( y = -2x \) to find \( y \)

Now that we know \( x = 2 \), we substitute this value into the equation \( y = -2x \). So \( y = -2\times2 = -4 \).

Answer:

The solution to the system is \( x = 2 \), \( y = -4 \) (or as an ordered pair \( (2, -4) \))