10. Simultaneous Equations
A set of N independent equations in N unknowns is called a system of simultaneous equations.
This system can then be solved to determine the values of the N unknown variables.
To solve a system of simultaneous equations, simply eliminate one variable at a time till you are left with a simple linear equation with one variable.
Then solve that linear equation and substitute back to solve for the other variables one at a time.
e.g. \$2x+y=3\$, \$x+2y=3\$
First, we notice that the equations are independent. You cannot get one equation by multiplying the other with a constant.
Next, we multiply the second equation by 2. Now we get, \$2x+y=3\$, and \$2x+4y=6\$
Subtracting the first equation from the second, we get, \$(2x-2x)+(4y-y)=(6-3)\$ or \$3y=3\$
Solving this, we get \$y=1\$, substituting in the first equation, we get \$2x+1=3\$, which gives \$x=1\$
So we have solved the system of equations, giving \$x=1\$, and \$y=1\$.

To reiterate, in general, you need N independent equations to be able to solve for N unknowns.
However, in the GMAT, you will never be asked to solve a system of more than three equations at the most.
Some trick questions might require you to perform a transformation before you can solve them.
e.g.\$2/a+1/b=3\$, \$1/a+2/b=3\$
If you set \$x=1/a\$ and \$y=1/b\$, you end up with the same set of equations as from the previous example.
We already know the solution there was \$x=y=1\$. We now substitute back (we want the values for a and b, not x and y)
So we get, \$a=1/x=1/1=1\$ and \$b=1/y=1/1=1\$