Question

solve the system of equations y = 4x + 1 y = x^2 + 2x - 2 A. (-3,-13) and (1,3) B. (-3,13) and (1,-3) c. (1,3) and (-3,13) D. (-1,-3) and (3,13)

Answer 1

We can solve the system of equations by setting the expressions for y equal to each other:

4x + 1 = x^2 + 2x - 2

Simplifying and rearranging, we get:

x^2 - 2x - 3 = 0

Factoring, we get:

(x - 3)(x + 1) = 0

So the solutions for x are x = 3 and x = -1.

Substituting these values back into either equation, we get the corresponding values of y:

When x = 3, y = 4x + 1 = 13.

When x = -1, y = 4x + 1 = -3.

Therefore, the solution to the system of equations is (x,y) = (-1,-3) and (3,13).

The correct answer is (D).

Answer 2

Explanation:

Since each equaion is equal to 'y'....just equate them and solve for 'x'

4x+1 = x^2 + 2x -2 simplify

x^2 -2x -3 = 0 factor ( or use Quadratic Formula)

(x-3)(x+1) = 0 shows x = 3 or -1

sub these values into either one of the equations to calculate the corresponding 'y' :

when x = 3 y = 4x+1 y = 4(3) + 1 = 13

When x = -1 y = 4 (-1) +1 = -3

(3,13) and ( -1, -3)