Solve by elimination. -9X-3Y= -18, 3X+Y= 6 Everything cancels SB 4,-6

Question

I tried to solve by elimination, sustitution, etc but everything keeps cancelling out to 0=0. I know X=4 and Y=-6 works.

 

Thanks, Ron

Answer 1

If everything cancels out then it means you really only have one equation because -9x-3y=-18 and 3x+y=6 are the same thing.

3x + y = 6

multiply both sides by -3

-9x -3y = -18

same thing

That means there is not a unique solution (only one possible value for x and for y).  That means there are an infinite number of solutions.

You can pick any value for x and get a y value that works:

x = 437 (example)

3*437 + y = 6

1311 + y = 6

y = -1305

Answer:  x = 437, y = -1305

 

You can pick any value for y and get an x value that works:

y = 36 (example)

3x + y = 6

3x + 36 = 6

3x = -30

x = -10

Answer:  x = -10, y = 36