Question

use a graph to determine the number of solutions of the system.
y = -x + 2
y = -5x + 9
one solution
no solution
infinitely many solutions

Explanation:

Step1: Analyze the slopes of the two lines.

The first equation is \( y = -x + 2 \), so its slope \( m_1=-1 \). The second equation is \( y=-5x + 9 \), so its slope \( m_2=-5 \). Since \( m_1
eq m_2 \), the two lines are not parallel and not coincident.

Step2: Determine the number of solutions.

For a system of linear equations in two variables, if the two lines have different slopes (i.e., they are not parallel and not coincident), they will intersect at exactly one point. So the system has one solution.

Answer:

one solution