Answer:x = - 3 twice
Step-by-step explanation:
6x + y = –16 - - - - - - 1
y + 7 = x^2 - - - - -2
From equation 1, y = - 16 - 6x
Substituting y = - 16 - 6x into equation 2, it becomes
- 16 - 6x + 7 = x^2
x^2 + 6x + 9 = 0
x^2 + 6x + 9 = 0
Solving the quadratic equation by factorization method, we will pick two numbers such that their sum is 6x and their product is 9. So we will pick 3x and 3x. It becomes
x^2 + 3x + 3x + 9 = 0
x(x + 3) + 3(x + 3) = 0
(x + 3)(x + 3) = 0
x + 3 = 0 or x + 3 =0
x = -3 or x =-3
Therefore, x = - 3 twice
Substituting x = - 3 into equation 1, it becomes
6 × -3 + y = –16
-18 + y = - 16
y = - 16 + 18
y = 2
