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Solve the system of equations

 Jun 8, 2018
 #1
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y  = x^2  - 3x + 4

x + y  =  4    ⇒   y  =  4 - x

 

Set the y's equal

 

x^2 - 3x  + 4   =  4  - x         subtract 4 from both sides

 

x^2  - 3x    =  - x          add x to both sides

 

x^2  - 2x  =   0        factor

 

x ( x - 2)  = 0

 

So.....setting each factor to 0 and solving, we have

 

x  = 0                   x  - 2   = 0   add 2 to both sides

 

                             x  = 2

 

So....the solutions are   x   = 0    and x  = 2

 

 

cool cool cool

 Jun 8, 2018

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