SOLUTION: Which ordered pair is a solution of the system of equations y=x^2-x-20 and y=3x-15? I did do some work i did y=x^2-x-20 y=(x^2-5x)(4x-20)

Question 289082: Which ordered pair is a solution of the system of equations y=x^2-x-20 and
y=3x-15?
I did do some work i did
y=x^2-x-20
y=(x^2-5x)(4x-20)
y= x(x-5) 4(x-5)= y=(x+4)(x-5)
and
y=3x-15
y=3(x-5)
but i don't know what to do from there, i would appreciate the help
Found 2 solutions by Fombitz, dabanfield:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Since they both equal y, set them equal to each other and solve for x.
Then go back and solve for y.
You're solving for the intersection of a line and a parabola.

You can factor

Two solutions:

Then use either y,

(5,0)
.
.
.

(-1,-18)
.
.
.
Graphically

Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
Which ordered pair is a solution of the system of equations y=x^2-x-20 and
y=3x-15?
I did do some work i did
y=x^2-x-20
1.) y=(x^2-5x)(4x-20)
y= x(x-5) 4(x-5)= y=(x+4)(x-5)
and
y=3x-15
y=3(x-5)
but i don't know what to do from there, i would appreciate the help
Your factoring at 1.) is not correct.
Here's another approach:
2.) y = x^2 - x - 20
3.) y = 3x - 15
From 2.) we know we can substitute 3x - 15 for y in equation 1.)
3x - 15 = x^2 - x - 20
x^2 - 4x - 5 = 0
(x - 5)*(x + 1) = 0
x = 5 and x = -1 are solutions for x.
Substituting x = 5 in 3.) we have:
y = 3*5 - 15
y = 15 - 15 = 0
So the point (5,0) is the first "possible" solution to the system.
The other solution, substituing -1 for x:
y = 3*(-1) - 15
y = -3 - 15 = -18
So the point (-18, -1) is the seocnd possible solution to the system.
Let's check each soluiton in 2.):
First (5,0):
Does 0 = 5^2 - 5 - 20?
5^2 - 5 - 20 = 25 - 5 - 20 = 0
Yes, so (5,0) is a solution to both equations.

How about (-18,-1)?
Does -1 = (-18)^2 - 18 - 20
(-18)^2 - 18 - 20 = 324 - 38 = 286
286 is not equal to -1 so (18,-1) is not a solution to the system.

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