Suppose you are asked to solve the following system:
You want to solve one of the equations for one of the variables. If possible, I would solve for a variable with coefficient of 1. In this case there is no such variable, so I decide to solve the first equation for x. (There is no "right" choice; some choices might be simpler algebraically or arithmetically, but the method is general.)
We take this expression for x and substitute it into the second equation. (You must substitute into the other equation -- otherwise you have an identity i.e. you will get a statement that is always true.)
`-3(5/2-3/2y)+7y=11` ** Substituting in place of "x" **
Notice that the new equation involves only one variable, so it is amenable to standard techniques.
Then `x=5/2-3/2y` ==>`x=5/2-3/2(37/23)`
The solution will be `x=2/23,y=37/23`