Question

Solve the system of equations:

y= 2x - 5
y= x² - 5

A. (0,5) and (2, 2)
B. (0,-5) and (2, -1)
C. (-1, -7) and (4, 3)
D. (-1,-4) and (3, 4)

Answer 1

To solve the given system of equations, we substitute the y-value from the first equation into the second equation and solve for x. The solutions are then used to find the corresponding y-values. The system of equations has two solutions: (0, -5) and (2, -1).

Step-by-step explanation:

To solve the system of equations y = 2x - 5 and y = x² - 5, we can substitute the value of y from the first equation into the second equation.

Substituting y = 2x - 5 into y = x² - 5, we get 2x - 5 = x² - 5.

Simplifying this equation, we have x² - 2x = 0.

Factoring out x, we get x(x - 2) = 0.

Setting each factor equal to zero, we have x = 0 and x - 2 = 0.

Therefore, the solutions are x = 0 and x = 2.

Substituting these values back into y = 2x - 5, we find the corresponding values of y to be y = -5 and y = -1.

So, the system of equations has two solutions: (0, -5) and (2, -1).