Solve the system of equations: y=2x-5. y=x^2-5

(0, -5) and (2, -1)

Step-by-step explanation:

Since both equations have already been solved for y, the substitution method is the easiest approach here.  Set the two equations equal to each other:

y = 2x - 5 = x^2 - 5 = y

Focusing on the variable x only, we get 2x - 5 = x^2 - 5.

Adding 5 to both sides results in 2x = x^2.

Factoring this result, we get x(2 - x)  = 0, whose solutions are

x = 0 and x = 2.

Now find the corresponding y-values:

If x = 0, then y = 2(0) -5, or y = -5;

If x = 2, then y = 2(2) - 5, or y = -1

Writing the solutions as coordinate pairs:  (0, -5) and (2, -1)