Here's the rule:
To solve a system of 2 variables, one needs 2 distinct linear equations.
"Distinct" means different.
For example:
2x + 4y = 10
and
8y - 20 = -4x
are actually the same equation, rearranged. Therefore, they would be insufficient to solve for x and y.
"Linear" means no variable with an exponent other than 1.
For example:
x^2 = 25
is one equation with 1 unknown, but x has two possible values: +5 and -5.
There are also many cases where one doesn't need as many equations as variables. If one is only solving for part of a system or if one is solving for a relationship instead of an actual value, one can often get away with fewer than the usual number of equations.
For example:
What's the value of x?
(1) x + 2y + 3z = 10
(2) 4y + 6z = 18
Even though we only have 2 equations with our 3 variables, we can divide statement (2) by 2 to get 2y + 3z = 9; now we can sub in the value for 2y + 3z into statement (1) and all we're left with is x and some numbers.
What's the value of a - b?
(1) a + b = 15
(2) 3a - 3b = 21
One might assume that the answer would be (C), but statement (2) is good enough by itself since we can divide through by 3 to get:
a - b = 7
which is exactly what the question is asking for.
