Answer:
(0, 6) and (-5, 1)
Step-by-step explanation:
It is easy enough to try the offered solutions in the equations. The incorrect ones fail to satisfy the first equation. Trying the first offered point for each answer, we can see whether y = x +6:
a: 6 ≠ 2 +6
b: -5 ≠ -7 +6
c: 6 ≠ -5 +6
d: 6 = 0 +6 . . . . . this is the correct answer choice
e: 2 ≠ 5 +6
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If you actually want to figure the answer, I recommend a graphing calculator as a quick and easy way to do it. Analytically, you can equate the expressions for y and solve the resulting quadratic:
... y = y
... x +6 = x^2 +6x +6 . . . . substitute the two expressions for y
... 0 = x^2 +5x . . . . . subtract the left side
... 0 = x(x +5) . . . . . . factor
Values of x that make this product zero are x=0 and x=-5. Corresponding values of y can be found using the first equation: add 6 to x.
... (x, y) = (0, 6), (-5, 1)
