Substitution Method

Question

Solve by the substitution method.
2x − 6y = −18
−x + 3y = 9

(x,y)

Answer 1

Hi Jane

 

I do not know if there is any typing error in one of the above equations. But assuming that is not the case, we have the following situation:

 

- x + 3y = 9        (1a)

 

2x  -6y   = -18    (2)

 

If you multiply the equation (1a) by (-2), you have:

 

2x  - 6y = -18    (1a)

 

It is exactly the same equation that (2).  Then, it means that the original equations (1) and (2) are both parallel lines and there is not solution. Because parallel lines never intersect.

 

 

 

 

Answer 2

 

Given:

    2x - 6y = -18    (Equation 1)

    -x + 3y = 9       (Equation 2)

 

Simplify equation 1 by dividing both sides (all terms) by 2

 

    x - 3y = -9    (Equation 1)

 

Solving equation 2 for x,

 

     -x + 3y = 9

     -x = 9 - 3y

      x = 3y - 9

 

Substitutiong "3y-9" for x in equation 1

 

     x - 3y = -9

     3y-9 -3y = -9

     0 - 9 = -9

     -9 = -9

 

Since the variable has been eliminated and we end up with a true statement,  we have infinitely many solutions