Question

What are the solutions to the system of equations?

y=x^2−5x+6
y=−4x+6
A. (−1, 0) and (0, 6)
B. (−1, 0) and (6, 0)
C. (0, −1) and (6, 0)
D. (0, 6) and (1, 2)

Answer 1

d

Explanation:

y=0^2-5x0+6=0+0+6=6

y=-4x0+6=0+6=6

y=1-5+6=2

y=-4+6=2

Answer 2

Answer: D. (0, 6) and (1, 2)

Explanation:

Make both equations equal to each other and solve for x:

`x^2-5x+6=-4x+6\\x^(2)-5x+4x+6-6=0\\x^2-x=0\\x(x-1)=0\\x=0\\x=1`

Substitute these values into any of the original equations to find the y-coordinates, as following:

`y=-4(0)+6=6\\y=-4(1)+6=2`

Therefore, the solutions are: (0, 6) and (1, 2)