SOLUTION: Solve the system {{{y=12x-19}}} {{{y=x^2+5x-7}}}

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Question 135442: Solve the system

y=12x-19

y=x%5E2%2B5x-7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
y=12x-19

y=x%5E2%2B5x-7



12x-19=x%5E2%2B5x-7 Set the two equations equal to one another



0=x%5E2%2B5x-7-12x%2B19 Subtract 12x from both sides. Add 19 to both sides.



0=x%5E2-7x%2B12 Combine like terms


%28x-4%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-4=0 or x-3=0

x=4 or x=3 Now solve for x in each case


So our x values are

x=4 or x=3



y=12x-19 Start with the first equation

y=12%284%29-19 Plug in x=4

y=29 Simplify


So the first ordered pair is (4,29)



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y=12x-19 Start with the first equation

y=12%283%29-19 Plug in x=3

y=17 Simplify


So the second ordered pair is (3,17)




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Answer:

So the solutions are
(4,29) or (3,17)