Solve the system. y = - x + 7 y = (1)/(2)(x - {3})^(2) ​

Question

Solve the system.


`y = - x + 7`

`y = (1)/(2)(x - {3})^(2)`
​

Answer 1

That is the answer , hope this helps.!

Answer 2

Explanation:

`y = (1)/(2)*(x - 3)^(2)\\\\\\2y = (x-3)^(2)\\\\\\2y = x^(2)-2*x*3 + 3^(2)\\\\\\2y = x^(2) - 6x + 9 \ --------------(I)`

y = -x + 7 -------------(II)

Plugin y = -x + 7 in equation (I)

2(-x + 7) =x² - 6x + 9

-2x + 14 =x ² - 6x + 9

x² - 6x + 9 = -2x + 14

x² - 6x + 9 + 2x - 14 = 0

x² - 4x - 5 = 0

x² -5x + x - 5 = 0

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

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

x- 5 = 0 ; x + 1 = 0

x = 5 ; x = -1

When x = 5 ⇒ y = -5 + 7 = 2

When x = -1 ⇒ y = -(-1) + 7 = 1 + 7 = 8

Solution (5 , 2) & (-1 , 8)