Question

check graphically whether the pair of equation 3x-2y+2=0 and 3/2x-y+3=0 is consistent. also find the coordinates of the points where the graphs meet the y-axis

Answer 1

Answer: Inconsistent, (0, 1), (0, 3)

Answer 2

3x - 2y + 2 = 0 → -2y + 2 = -3x → -2y = -3x - 2 → y =
`(3)/(2)`x + 1

`(3)/(2)`x - y + 3 = 0 → -y + 3 = -
`(3)/(2)`x → -y = -
`(3)/(2)`x - 3 → y =
`(3)/(2)`x + 3

These two equations have the same slope but different y-intercepts so they are parallel lines. (aka inconsistent).

Answer: Inconsistent, (0, 1), (0, 3)