Question

Please help idk this one !!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

Given system of equation:
y+4=x² Equation 1
y-x=2 Equation 2
Isolate y from equation 2.
y=x+2 Substitute value of y in equation 1.
x+2+4=x²
x+6=x²
x²-x-6=0
Solve for x.
x²-3x+2x-6=0
x(x-3)+2(x-3)=0
(x-3)(x+2)=0
x-3=0 or x=3
and
x+2=0 or x=-2
Substitute value of x in y=x+2
y=-2+2=0
and
y=3+2=5
So solutions are (-2,0) and (3,5)

Answer: (-2,0) and (3,5)