Question

What is the solution to the system of equations?

2/3x - 1/3y = -2
-2x + y = -6

There is no solution.
There are infinitely many solutions.
There is only one solution, (2, –2).
There is only one solution, (–2, –10).

Answer 1

There is no solution.

Rewrite -2x + y = -6 so it starts with y =...

y = 2x - 6

Substitute that in 2/3x - 1/3y = -2 gives:

2/3x - 1/3*(2x -6) = -2

2/3x - 2/3x + 2 = -2

0 + 2 = -2

This statement is not true, and that means there is no solution.