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Solve the system y = (x - 2)^2 + 2, y + 4 = 3x.

 

Please show steps.

 Jul 19, 2020
 #1
avatar+26675 
+1

y = 3x-4          and   y = x^2 -4x+4+2     equate them

x^2 - 4x +6 = 3x-4

x^2-7x+10 = 0

(x-5)(x-2) = 0        so x = 5   and 2    

                 use these values of 'x' in one of the equations to compute the coresponding 'y' s

 Jul 19, 2020
 #2
avatar+1034 
+2

To start, we can set y from the second equation to 3x-4. Plugging this in to the first equation gives us 3x-4 = (x-2)^2+2.

From here, we can add 4 to both sides and get 3x = (x-2)^2+6

Multiplying out (x-2)^2, we get x^2-4x+4.

Now, our equation is 3x = x^2-4x+10. Subtracting 3x from both sides will give us 0 = x^2-7x+10. Can you solve the quadratic from here?

 Jul 20, 2020

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