Question

PLSSSS HELPPP>> Show work solve the sysytem- y=1/2x^2+4x+4 y=-4x+12 1/2

Answer 1

The solution is (-17,80.5) and (1,8.5)

Explanation:

Equation 1 :
`y=(1)/(2)x^2+4x+4`

Equation 2:
`y = -4x+12.5`

Substitute the value of y from equation 2 in equation 1

Equation 1 :
`y=(1)/(2)x^2+4x+4`

After substitution :

`-4x+12.5=(1)/(2)x^2+4x+4\\(1)/(2)x^2+8x+4-12.5=0\\(1)/(2)x^2+8x-8.5=0\\x^2+16x+17=0\\x=-17,2`

Substitute the value of x = -17

y = -4x+12.5

y = -4(-17)+12.5

y=80.5

Substitute the value of x = 1

y = -4(1)+12.5

y=8.5

Hence the solution is (-17,80.5) and (1,8.5)