Question

solve the system of equations graphed on the coordinate axes below.
$y = \frac{4}{3}x + 4$
$y = -\frac{1}{2}x - 7$

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other:
\( \frac{4}{3}x + 4 = -\frac{1}{2}x - 7 \)

Step2: Multiply through by 6 to eliminate fractions

Multiply each term by 6 to get rid of the denominators (3 and 2):
\( 6 \times \frac{4}{3}x + 6 \times 4 = 6 \times (-\frac{1}{2}x) + 6 \times (-7) \)
Simplify each term:
\( 8x + 24 = -3x - 42 \)

Step3: Add \( 3x \) to both sides

\( 8x + 3x + 24 = -3x + 3x - 42 \)
Simplify:
\( 11x + 24 = -42 \)

Step4: Subtract 24 from both sides

\( 11x + 24 - 24 = -42 - 24 \)
Simplify:
\( 11x = -66 \)

Step5: Divide both sides by 11

\( x = \frac{-66}{11} = -6 \)

Step6: Substitute \( x = -6 \) into one of the original equations (e.g., \( y = \frac{4}{3}x + 4 \))

\( y = \frac{4}{3}(-6) + 4 \)
Simplify:
\( y = -8 + 4 = -4 \)

Answer:

The solution to the system is \( x = -6 \), \( y = -4 \) or the ordered pair \( (-6, -4) \)