SOLUTION: Solve the system by substitution {{{y=x^2-4}}} {{{y=6x-13}}}

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Question 135530: Solve the system by substitution
y=x%5E2-4
y=6x-13
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
y=x%5E2-4
y=6x-13


x%5E2-4=6x-13 Plug in y=x%5E2-4 into the second equation


x%5E2-4-6x%2B13=0 Get all terms to left side


x%5E2-6x%2B9=0 Combine like terms


%28x-3%29%28x-3%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-3=0 or x-3=0

x=3 or x=3 Now solve for x in each case


Since we have a repeating answer, our only answer is x=3


y=6x-13 Go back to the second equation


y=6%283%29-13 Plug in x=3


y=5 Simplify


Answer:

So the solution is (3,5)