Question

Suri makes $15 per hour and gets a weekly bonus of $25. Juan makes $14 per hour and gets a weekly bonus of $50. Is it possible for Suri and Juan to make the same amount of wages, y, by working the same number of hours, x, in one week?
Yes, because the slopes of the equations are different so the system of equations will have one solution.
No, because the slopes of the equations are different so the system of equations will have no solutions.
Yes, because the slopes of the equations are the same so the system of equations will have infinitely many solutions.
No, because the slopes of the equations are the same so the system of equations will have no solutions.

Answer 1

Yes — the first option.

Set 15x + 25 = 14x + 50 ⇒ x = 25, y = 15(25) + 25 = 400. The slopes (15 and 14) are different, so the two lines meet in exactly one point.