Question

Match the system of equations to the number of solutions it has.(4 points)

y=2/3x−1 and y=2/3x−2

y=5x+7 and 3y−15x=18

3x+6=y and y=−1/3x−4

x−2y=6 and 3x−6y=18

Answer 1

1. y=2/3x−1 and y=2/3x−2
This system of equations has no solution because the two equations represent parallel lines with the same slope but different y-intercepts.

2. y=5x+7 and 3y−15x=18
This system of equations has one unique solution, where the two equations intersect at a single point.

3. 3x+6=y and y=−1/3x−4
This system of equations has one unique solution, where the two equations intersect at a single point.

4. x−2y=6 and 3x−6y=18
This system of equations has infinitely many solutions because one of the equations is a multiple of the other. The lines coincide and overlap, resulting in infinite points of intersection.