Answer:
-1 and 0
Explanation:
This is a set of simultaneous equations. To solve them, you need to substitute one into the other. The easiest way to do this would be to rearrange x - y = -6 to make x the subject:
x = -6 + y
x = y - 6
Now we can substitute this equation into y = -x^2 + 5x + 6:
y = -(y - 6)^2 + 5(y - 6) + 6
Now simplify this equation, and rearrange to make it equal to 0:
y = -y^2 + 12y - 36 + 6
y = -y^2 + 12y - 30
0 = -y^2 + 12y - y - 30
-y^2 + 11y - 30 = 0
Now solve this quadratic equation to obtain two solutions:
y = 5, y = 6
Now substitute these values back into one of the starting equations to find the respective values for x:
When y = 5:
x - 5 = -6
x = -1
When y = 6
x - 6 = -6
x = 0
Therefore, the x solutions are -1 and 0.