Answer: the solutions are
(3/2, 5)
(- 1, 0)
Step-by-step explanation:
The given system of equations is expressed as
y = 2x² + x - 1- - - - - - - - - - - - - 1
y = 2x + 2- - - - - - - - - - - - - 2
We would apply the method of substitution by substituting equation 2 into equation 1. It becomes
2x + 2 = 2x² + x - 1
2x² + x - 2x - 1 - 2 = 0
2x² - x - 3 = 0
2x² + 2x - 3x - 3 = 0
2x(x + 1) - 3(x + 1)
2x - 3 = 0 or x + 1 = 0
2x = 3
x = 3/2 or x = - 1
Substituting x = 3/2 or x = - 1 into equation 2, it becomes
y = 2 × 3/2 + 2 or y = 2 × - 1 + 2
y = 5 or y = 0
