Question

Solve each system of equations by substitution or elimination.

y=x^2-2x-1
y=-x^2-2x-1

Show all steps and explain what method you chose.

Answer 1

x = 0, y = -1.

Explanation:

y = x^2 - 2x - 1

y = -x^2 - 2x - 1

Use elimination:

Subtract the 2 equations:

0 = x^2 - (-x^2) - 2x - (-2x) - 1 - (-1)

Simplifying:

0 = x^2 + x^2 - 2x + 2x - 1 + 1

0 = 2x^2

x = 0 .

Substitute this into the first equation:

y= 0^2 - 2(0) - 1

y = -1.