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):
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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