Question

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

Answer 1

Answer:

$x = 4$

$y = -5$

Step-by-step 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 $y = -5x^2 + 40x - 85$

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

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

$y = -80 + 160 - 85$

$y = -5$