Stumped by a past assessment question

Question

If $x - 12y = -210$ and $x - 6y = 90$, then what is $x$ equal to?

Answer 1

$x-6y=90/\cdot (-2)$

Then you add one equation to another and you get $-x=-390,$ so $x=390.$

Answer 2

This is a system of equations with two unknowns $x$ and $y$.

You first isolate for one of the unknowns in one of the equations, in this case I chose $x$ as it has no coefficient, and the first equation for no particular reason. $x-12y = -210 \implies x= 12y-210$.

You then substitute it into the second equation as follows:
$x-6y=90 \implies (12y-210)-6y = 90$
$\therefore 6y-210 = 90$
$\therefore 6y=300$
$\therefore y = 50$

Substituting this back into the first equation, we get $x= 12(50)-210$.

Therefore, $x=390$ .

Though it may seem a little challenging at first if you just started learning it, you'll soon get a feel for substitution and elimination, as well as for which variables to isolate for / to solve for first. Just practice a lot of them, and in no time they'll become second nature.