Question

x: number of minutes
y: number of steps
how many solutions does this system of equations have?
one solution
infinitely many solutions
no solution
kellan: y = 150 - 15x
luka: y = 10x

Explanation:

Step1: Recall solution types for linear systems

A system of linear equations (two lines) has one solution if the lines intersect at one point, infinitely many if they are the same line, and no solution if they are parallel (never intersect).

Step2: Analyze the graph

The graph shows two lines: \( y = 150 - 15x \) (Kellan) and \( y = 10x \) (Luka). These lines intersect at one point (where their \( x \) and \( y \) values are equal). Parallel lines have the same slope; here, slopes are \( -15 \) and \( 10 \) (different), so not parallel. They aren't the same line (different equations, slopes, y-intercepts). So they intersect once.

Answer:

One solution