Question

Solve the system by substitution. y=3x^2-2x-1 y=x-1

A. no solution
B. (-1,-2)
C. (4,3), (2,1)
D. (0,-1), (1,0)

Answer 1

the answer is D (0,-1), (1,0). These are the only two places where both lines intercept.

Answer 2

Option D.

Explanation:

The given equations are y = 3x² - 2x - 1 -------(1)

and y = x - 1 --------(2)

To evaluate the solutions of the equation by substitution method we will substitute the value of y from equation (2) to equation (1)

x - 1 = 3x² - 2x - 1

3x² - 2x - x - 1 + 1 = 0

3x² - 3x = 0

3x(x - 1) = 0

x = 0

(x - 1) = 0

x = 1

For x = 0,

y = 0 - 1 = -1

for x = 1,

y = 1 - 1 = 0

Therefore, solutions for the equations are (0, -1) and (1, 0).

Option D is the answer.