Question

What are the solutions to the system of equations? {y=2x2−8x+5y=x−2 (3.5, 0.5) and (1, −1) (7, 5) and (0.5, −1.5) (3.5, 1.5) and (1, −1) (3.5, 1.5) and (−1, −3)

Answer 1

`(1,-1)` and
`(3.5,1.5)`

Explanation:

Given

`y = 2x^2 - 8x+5`

`y = x - 2`

Required

Determine the solution

Substitute x - 2 for y in
`y = 2x^2 - 8x+5`

`x - 2 = 2x^2 - 8x+5`

Collect like terms

`0 = 2x^2 - 8x - x + 5 + 2`

`0 = 2x^2 - 9x + 7`

Expand the expression

`0 = 2x^2 - 7x - 2x+ 7`

Factorize

`0 = x(2x - 7) -1(2x - 7)`

`0 = (x-1)(2x - 7)`

Split the expression

`x - 1 = 0` or
`2x - 7 = 0`

Solve for x in both cases

`x = 1` or
`2x = 7`

`x = 1` or
`2x/2 = 7/2`

`x = 1` or
`x = 3.5`

Recall that

`y = x - 2`

When
`x = 1`

`y = 1 -2`

`y = -1`

When
`x = 3.5`

`y = 3.5 - 2`

`y = 1.5`

Hence, the solution is;

`(1,-1)` and
`(3.5,1.5)`