Question

solve the following system of equations graphically on the set of axes below.
$y = 2x - 5$
$y = -x - 8$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection algebraically (optional)

To solve the system \( y = 2x - 5 \) and \( y = -x - 8 \), set them equal:
\( 2x - 5 = -x - 8 \)
Add \( x \) to both sides: \( 3x - 5 = -8 \)
Add 5 to both sides: \( 3x = -3 \)
Divide by 3: \( x = -1 \)

Substitute \( x = -1 \) into \( y = 2x - 5 \):
\( y = 2(-1) - 5 = -2 - 5 = -7 \)

Step2: Graph \( y = 2x - 5 \)

• Y-intercept: When \( x = 0 \), \( y = -5 \). Plot \( (0, -5) \).
• Slope: \( 2 \) (rise 2, run 1). From \( (0, -5) \), move right 1, up 2: \( (1, -3) \). Plot this point. Draw the line through these points.

Step3: Graph \( y = -x - 8 \)

• Y-intercept: When \( x = 0 \), \( y = -8 \). Plot \( (0, -8) \).
• Slope: \( -1 \) (rise -1, run 1). From \( (0, -8) \), move right 1, down 1: \( (1, -9) \). Plot this point. Draw the line through these points.

The lines intersect at \( (-1, -7) \), which is the solution.

Answer:

The solution to the system is \( \boldsymbol{(-1, -7)} \).