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What are the solutions to the system of equations?   y=2x^2−6x+3        (both of the y= are in the one bracket)

                                                                                  {

                                                                                   y=x−2

(1, −1) and (5, 3)

(3, 1) and (2.5, 0.5)

(2.5, 0.5) and (4, 2)

(1, −1) and (2.5, 0.5)

 Aug 2, 2019
 #1
avatar+104937 
+2

y = 2x^2 - 6x + 3

y = x - 2     

 

Set the y's equal  and solve for  x

 

2x^2 - 6x + 3  =  x - 2         subtract x , add 2    from/to each side

 

2x^2 - 7x + 5  = 0          factor, if possible

 

(2x -5) ( x - 1)  = 0

 

Set each factor  to 0   and solve  for  x

 

2x  - 5  = 0                   x  - 1  =0

2x  = 5                         x = 1

x = 5/2 = 2.5                x  = 1

 

So    y  = x - 2 = 2.5 - 2  = 0.5        or   y = x - 2 =   1 - 2  = -1

 

So  {x,y}   =  { 2.5, 0.5}     or  { 1, -1 }         

 

 

 

cool cool cool

 Aug 2, 2019

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