Solve the system y = - x + 7 and y = 0.5 (x - 3) 2

explain the answer

x=5, x=-1

Step-by-step explanation:

Since both equations are equal to y, we can set them equal to each other

y = - x + 7 and y = 0.5 (x - 3) 2

-x + 7 = 0.5 (x - 3) ^2

Distribute the right hand side by Foiling

-x+7 =.5 (x^2 - 3x-3x+9)

Combine like terms

-x+7 =.5 (x^2 - 6x+9)

Distribute the. 5

-x+7 =.5x^2 - 3x+4.5

Add x to each side

-x+x+7 =.5x^2 - 3x+x+4.5

7 =.5x^2 - 2x+4.5

Subtract 7 from each side

7 - 7=.5x^2 - 2x+4.5-7

0 =.5x^2 - 2x-2.5

Multiply by 2 to clear the decimals

0 = x^2 - 4x - 5

Factor

0 = (x-5) (x+1)

Using the zero product property

x-5=0 x+1 = 0

x=5, x=-1