Originally Posted by **ThePerfectHacker**

I do one for you but you have to promise me to try the other three.

These are your equations,

$\displaystyle \left\{ \begin{array}{c}x+y=33 \\ 2x-y=18$

There five ways to solve these problem.

I will only mention two which I believe you should know: addition method, substitution method.

**Addition method**

Add the two equations, note that $\displaystyle x+2x=0$, $\displaystyle y+(-y)=0$, $\displaystyle 33+18=51$

Thus,

$\displaystyle 3x=51$ from here divide both sides by three,

$\displaystyle x=17$, thus, $\displaystyle y=16$

*The entire purpose of the addition method is when you add your equation you eliminate one of the variables and are left with one*.

**Substitution method**

Solve and equation for any variable, i.e. first equation for 'x' thus,

$\displaystyle x=33-y$

Now substitute that into the second equation,

$\displaystyle 2(33-y)-y=18$, you substituted 'x' for 'y' and hence eliminated a variable.

Open parantheses,

$\displaystyle 66-2y-y=18$

Subtract 66 and combine 'y' to get,

$\displaystyle -3y=-48$ divide by (-3) to get,

$\displaystyle y=16$ thus, $\displaystyle x=33-16=17$