Question

solve the system of equations graphed on the coordinate axes below.
y = \\(\frac{1}{2}\\)x + 2
y = -3x - 5

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other:
\( \frac{1}{2}x + 2 = -3x - 5 \)

Step2: Solve for \( x \)

First, multiply both sides by 2 to eliminate the fraction:
\( x + 4 = -6x - 10 \)
Add \( 6x \) to both sides:
\( 7x + 4 = -10 \)
Subtract 4 from both sides:
\( 7x = -14 \)
Divide by 7:
\( x = -2 \)

Step3: Substitute \( x \) back to find \( y \)

Substitute \( x = -2 \) into \( y = \frac{1}{2}x + 2 \):
\( y = \frac{1}{2}(-2) + 2 \)
\( y = -1 + 2 \)
\( y = 1 \)

Answer:

The solution to the system is \( x = -2 \), \( y = 1 \) or the ordered pair \( (-2, 1) \)