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Given that $3x + y = 10$ and $x + 3y = 14$, find $10x^2 + 12xy + 10y^2$.

 Jun 15, 2019
 #1
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Given that 3x + y = 10 and x + 3y = 14, find 10x^2 + 12xy + 10y^2.

 

3x + y  = 10      (1)

x + 3y = 14   ⇒  -3x - 9y = -42    (2)     add (1) and (2)

 

-8y  =  -32    divide through by -8

y = 4

 

So  using (1)     3(x) + 4  = 10

                         3(x)  = 6

                            x = 2

 

So     

10x^2 + 12xy + 10y^2    = 

10 (2)^2 + 12 (2)(4) + 10(4)^2  =  

40 + 96 + 160  =

296

 

 

cool cool cool

 Jun 15, 2019

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