Question

Compare the slopes and y-intercepts of the graphs of the equations in the linear system y - 3x = 2 and 5y = 15x + 2.5 to determine whether the system has one solution, no solution, or infinitely many solution. Explain.

Answer 1

y-3x=2

• y=3x+2

5y=15x+2.5

• y=3x+0.5

As we can see

slopes are equal i.e 3

Hence

lines are parallel so no solutions

Answer 2

• No solution

Explanation:

Convert both equations into slope-intercept form:

• y - 3x = 2 ⇒ y = 3x + 2
• 5y = 15x + 2.5 ⇒ y = 3x + 0.5

As we see both lines have same slopes m = 3 but different y-intercepts: 2 and 0.5.

It means the lines are parallel and never intersect hence no solution to the system.