Question

What is the solution set of the system of equations x+y=5 and y=x^2-25

Answer 1

The solution set is basically when are they equal. to figure this out we must set them equal. So so we will move some stuff around

x+y=5
y=5-x

y=x^2-25

we know that when they are equal their x and y values are equal. So so we know that their y values are the same so we can say:

y=y

this does not direarly help but looking above we know what both of the y's equal. so:

5-x = x^2-25

we want to set this equal to zero

0 = x^2 +x - 30

now we factor

0 = (x + 6) * (x - 5)

the only way to multiply 2 things together and get zero is for one of those things to equal 0. So so we know that to be zero one of the answers in parenthesis has to equal 0. so:

0 = (x + 6 =0) * (x - 5=0)

So now we solve for both parenthesis

x+6=0
x=-6

x-5=0
x=5

x=-6,5