Question

Solve these equations below simultaneously:y=x^2;y=x+2

Answer 1

Answer:

(x, y) = (2, 4) or (-1, 1)

Step-by-step explanation:

y = x^2

y = x + 2

=> x^2 = x + 2

Transfer all terms to the left, we have:

=> x^2 - x - 2 = 0

Perform some modifications, we have:

=> x^2 + x - 2x - 2 = 0

Let's group the left-side terms up.

=> x(x + 1) - 2(x + 1) = 0

=> (x - 2)(x + 1) = 0

=> x = 2 => y = x + 2 = 2 + 2 = 4

=> x = -1 => y = x + 2 = -1 + 2 = 1

=> Solution is (x, y) = (2, 4) or (-1, 1)

Hope this helps!