Question

Which represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.

(–2, 0)
(–2, 0) and (2, 0)
(–2, 0) and (3, 5)
no solutions

Answer 1

`(-2,0)` and
`(3,5)`

Explanation:

we have

`y+4=x^(2)` -----> equation A

Is a vertical parabola open upward

`y-x=2` ----> equation B

Is the equation of a line

we know that

The solution of the system of equations is the intersection point both graphs

Using a graphing tool

The intersection points are
`(-2,0)` and
`(3,5)`

see the attached figure

Answer 2

y + 4 = x^2 . . . (1)
y - x = 2 . . . (2)
From (2), y = 2 + x . . . (3)
Putting (3) into (1), gives
2 + x + 4 = x^2
x^2 - x - 6 = 0
(x + 2)(x - 3) = 0
x = -2 or x = 3
y = 2 - 2 = 0 or y = 2 + 3 = 5

Solution set is (-2, 0) and (3, 5)