Answer:
B. x=2, x=-3
Step-by-step explanation:
Hello,
We are given this system of equations:
y=4-x²
x-y=2
And we want to solve it for x.
There are a couple ways to solve systems of equations, but let's use substitution in this problem, which we will set one variable equal to an expression containing the other variable, use that expression to solve for the variable the expression contains in the other equation, then use the value of the solved variable to find the value of the other variable.
But in this case, we just need to find x, which is just one of the variables, so there's no need to find the values of y.
In x-y=2, subtract x from both sides.
-y=-x+2
Multiply both sides by -1.
y=x-2
Substitute y as x-2 in y=4-x².
x-2=4-x²
Add x² to both sides.
x²+x-2=4
Subtract 4 from both sides.
x²+x-6=0
Now factor using FOIL.
1 (coefficient in front of x) is the sum of the numbers used in the binomials, while -6 is their product.
Two numbers that add up to 1 but multiply to get -6 are -2 and 3.
So now factor:
(x-2)(x+3)=0
Split and solve:
x-2=0
x=2
x+3=0
x=-3
The solutions for x are x=2 and x=-3, which means the answer is B.
Hope this helps!
