Question

1. use elimination to solve the system of equations.

y = x - 6
y = -x - 2
a (-2, 4)
b (2, -4)
c (-4, 2)
d (4, -2)

Explanation:

Step1: Rewrite equations in standard form

Rewrite \( y = x - 6 \) as \( -x + y = -6 \) and \( y = -x - 2 \) as \( x + y = -2 \).

Step2: Add the two equations

Add \( -x + y = -6 \) and \( x + y = -2 \):
\( (-x + y) + (x + y) = -6 + (-2) \)
Simplify: \( 2y = -8 \).

Step3: Solve for y

Divide both sides by 2: \( y = \frac{-8}{2} = -4 \).

Step4: Substitute y into an equation

Substitute \( y = -4 \) into \( y = x - 6 \):
\( -4 = x - 6 \).
Add 6 to both sides: \( x = -4 + 6 = 2 \).

Step5: Verify the solution

Check \( (2, -4) \) in both equations:

• For \( y = x - 6 \): \( -4 = 2 - 6 \) (True).
• For \( y = -x - 2 \): \( -4 = -2 - 2 \) (True).

Answer:

B. (2, -4)