match the system of equations

1 ): 3x-2y=-1,-x+2y=3 (1,2)

2): 4x-3y=-1 , -3x+4y=6       (2,3)

3x+6y=6, 2x+4y=-4 ( no solution)

-3x+6y=-3, 5x-10y=5 infinite

Step-by-step explanation:

4x-3y=-1

-3x+4y=6  ( multiply first by 3 and second equation by 4)

12x-9y=-3

-12x+16y=24 subtract

7y=21

y=21/7=3

x=2, y=3 (2,3)

3x-2y=-1

-x+2y=3

solve by addition/elimination ( same as other equation):

multiply second equation by 3

3x-2y=-1

-3x+6y=9

4y=8

y=2

x=1

3x+6y=6, 2x+4y=-4 ( no solution)

-3x+6y=-3, 5x-10y=5 infinite

c

step-by-step explanation:

there is vertical asymptote at x = 2 and x = 0

vertical asymptote occurs at the points where the denominator is 0. so we can say that

x = 2 occurs when there is a factor (x-2) in the denominator, and

x = 0 occurs when there is a factor "x" in the denominator

thus, the denominator of the equation would have "x * (x-2)", this is option c only. that's the correct answer.