Question

question
solve the system of equations graphed on the coordinate axes below.
( y = -x - 8 )
( y = \frac{1}{3}x - 4 )

Explanation:

Step1: Set the equations equal

Since both equations are solved for \( y \), set \( -x - 8=\frac{1}{3}x - 4 \).

Step2: Add \( x \) to both sides

\( -8=\frac{1}{3}x+x - 4 \), simplify \( \frac{1}{3}x+x=\frac{4}{3}x \), so \( -8=\frac{4}{3}x - 4 \).

Step3: Add 4 to both sides

\( -8 + 4=\frac{4}{3}x \), which gives \( -4=\frac{4}{3}x \).

Step4: Solve for \( x \)

Multiply both sides by \( \frac{3}{4} \): \( x=-4\times\frac{3}{4}=-3 \).

Step5: Substitute \( x \) into one equation

Use \( y=-x - 8 \), substitute \( x = - 3 \): \( y=-(-3)-8=3 - 8=-5 \).

Answer:

The solution is \( (-3, -5) \)