Question

Solve the system of equations.

y=x+5
y=x2+5x−7


Enter your answers in the boxes.

4

5

6

7

Answer 1

(2, 7) or (-6, 1)

Explanation:

We are given two equations:

`y=x+5`; and

`y = x^2+5x-7`

Since y is the subject for both the equations so we can put the values of y equal to each other to get:

`x+5=x^2+5x-7`

`x^2+5x-x-7-5=0`

`x^2+4x-12=0`

Factorizing the expression to get:

`x^2-2x+6x-12=0`

`x(x-2)+6(x-2)=0`

`(x-2) (x+6) = 0`

`x=2, x= -6`

Putting x = 2 and x = -6 in any of the equations to get the values of y:

`y=x+5`

`y =2+5`

`y=7`

and

`y =(-6)+5`

`y=1`

Therefore, solution to these equation is (2, 7) or (-6, 1).