2x-2=y

Solve:  y  =  2x - 2     and     y  =  -3x² + x + 2

 

Set the right-sides of the equations equal to each other:

     2x - 2  =  -3x² + x + 2

 

Reduce the left-side to 0 by adding 2 to each side and subtracting 2x from each side:

           0  =  -3x² - x + 4

 

To make factoring easier, multiply both sides by -1:

     0  =  3x² + x - 4

 

     0  =  (3x + 4)(x - 1)

 

Solve:  3x + 4  =  0     --->     x  =  -4/3          and         x - 1  =  0     --->     x  =  1

 

Substituting these values back into the equation  y  =  2x - 2:

 

If  x = -4/3,  y = -4 2/3          and         if  x = 1,  y = 0