solve substitution method

Question

y=x^2

y-7x=-12

Answer 1

y = x²                    eq1

y - 7x = -12       eq2

 

Substitute eq1 into eq2.

 

x² - 7x = -12

 

Add 12 on both sides of equation to get the right side equal to zero. 

 

x² - 7x + 12 = 0

 

Factor the left side using FOIL method.

 

(x - 4)(x - 3) = 0

 

x = 4     and     x = 3

 

 

Substitute these x values into eq1.

 

y = 4²                   and         y = 3²

y = 16             and         y = 9

 

We will have two ordered pairs:  (4,16) and (3,9).

 

Let's substitute the x and y values of the two ordered pairs into eq2 to see if they check out.

 

16 - 7(4) = -12

16 - 28 = -12

    -12  = -12

 

True.

 

9 - 7(3) = -12

  9 - 21 = -12

     -12  = -12

 

True.

 

The two ordered pairs (3,9) and (4,16) are the solutions.