Question

Solve each system using substitution or elimination. Show all required work. -10x^2+80x+y=155 5x^2-40x+y=-85

Answer 1

`x = 4`

`y = -5`

Explanation:

Given

`-10x^2+80x+y=155`

`5x^2-40x+y=-85`

Required

Solve by substitution

Make y the subject in
`5x^2-40x+y=-85`

`5x^2-40x+y=-85`

`y = -5x^2 + 40x - 85`

Substitute
`y = -5x^2 + 40x - 85` in the first equation

`-10x^2+80x+y=155`

`-10x^2 + 80x -5x^2 + 40x - 85 = 155`

Collect Like Terms

`-5x^2-10x^2 + 80x + 40x - 85 - 155=0`

`-15x^2 + 120x-240=0`

Divide through by -15

`x^2 -8x + 16 = 0`

`x^2 - 4x - 4x + 16 = 0`

`x(x - 4) - 4(x - 4) = 0`

`(x - 4)(x - 4) = 0`

`x - 4\ = 0` or
`x - 4\ = 0`

`x = 4` or
`x = 4`

`x = 4`

Substitute 4 for x in
`y = -5x^2 + 40x - 85`

`y = -5(4)^2 + 40 * 4 - 85`

`y = -5*16 + 40 * 4 - 85`

`y = -80 + 160 - 85`

`y = -5`