Question

what are the two solutions to the system y= x^2 + 3x -4 y= 2x + 2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the solutions to the system of equations y = x^2 + 3x - 4 and y = 2x + 2, we can set the two equations equal to each other and solve for x.

x^2 + 3x - 4 = 2x + 2

Rearranging the terms to set the equation equal to zero:

x^2 + 3x - 4 - 2x - 2 = 0

x^2 + x - 6 = 0

Now we can factor the quadratic equation:

(x + 3)(x - 2) = 0

Setting each factor equal to zero to find the solutions for x:

x + 3 = 0 or x - 2 = 0

x = -3 or x = 2

Now that we have found the values for x, we can substitute them back into either equation to find the corresponding values of y:

When x = -3:
y = (-3)^2 + 3(-3) - 4
y = 9 - 9 - 4
y = -4

When x = 2:
y = 2(2) + 2
y = 4 + 2
y = 6

Therefore, the two solutions to the system of equations are (-3, -4) and (2, 6).