Question

Which represents the solution(s) of the graphed system of equations, y = x2 + x -2 and y = 2x - 2?
Ty
2
1
O (-2, 0) and (0, 1)
O (0, -2) and (1,0)
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Answer 1

Answer:

(0, -2) and (1, 0)

Step-by-step explanation:

y = x² + x - 2 and y = 2x - 2    

  y = x² + x - 2  ⇔ do not change;       y = x² + x - 2

  y = 2x - 2        ⇔ multiply by -1  ;        -y = - 2x + 2  

Now add the two equations:  

     y = x² + x - 2

(+)  -y = - 2x + 2                  

      0 = x² - 2x + x  + 0      

       0 = x² - x            

        0 =  x (x - 1)    Factor out x

     0 = x;  0 = x - 1    Set each factor = to 0 and solve.

      x = 0;   x = 1    

  Substitution the value of x into both equations and solve for y

If x = 0                                                 If x = 1

y = (0)² + 0 - 2  ;   y = 2(0) - 2               y = 1² + 1 - 2  ;  y = 2(1) -2

y = 0 +0 -2      ;     y =  0 - 2                  y = 1 + 1 -2    ;  y = 2 - 2

  y = -2   ;    y = -2                                   y =  0           ;   y = 0

Solutions to the question:  (0, -2) and (1, 0)