Question

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

Explanation:

Step1: Set the two equations equal

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

Step2: Subtract 7 from both sides

Subtract 7 from each side to simplify:
\( -\frac{3}{2}x=\frac{1}{3}x \)

Step3: Move x terms to one side

Subtract \( \frac{1}{3}x \) from both sides:
\( -\frac{3}{2}x-\frac{1}{3}x = 0 \)
Find a common denominator (6) to combine the fractions:
\( -\frac{9}{6}x-\frac{2}{6}x = 0 \)
\( -\frac{11}{6}x = 0 \)

Step4: Solve for x

Multiply both sides by \( -\frac{6}{11} \):
\( x = 0\times(-\frac{6}{11}) \)
\( x = 0 \)

Step5: Find y

Substitute \( x = 0 \) into one of the original equations, say \( y=\frac{1}{3}x + 7 \):
\( y=\frac{1}{3}(0)+7 \)
\( y = 7 \)

Answer:

The solution to the system is \( x = 0 \), \( y = 7 \) or the ordered pair \( (0, 7) \)