SOLUTION: Solve the following system of equations and show all work. y = x2 + 3 y = x + 5 (10 points)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve the following system of equations and show all work. y = x2 + 3 y = x + 5 (10 points)       Log On


   

Question 984450: Solve the following system of equations and show all work.
y = x2 + 3
y = x + 5 (10 points)
Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since they both equal y, set them equal to each other.
x%5E2%2B3=x%2B5
x%5E2-x-2=0
%28x-2%29%28x%2B1%29=0
Two solutions:
x-2=0
x=2
and
x%2B1=0
x=-1
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Now go back with each x and find the corresponding y value.
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You can verify by plugging the values in the equation or by graphing.
Here's a graph.
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Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
set the two equations equal to each other
x^2 + 3 = x + 5
x^2 -x - 2 = 0
factor polynomial
(x+1) * (x-2) = 0
therefore, x = -1 or 2
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check the answers
a) x = -1
(-1)^2 + 3 = -1 + 5
1 + 3 = 4
4 = 4
b) x = 2
2^2 + 3 = 2 + 5
4 + 3 = 7
7 = 7
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