# Can someone please give me an easier way to understand or how to do system equation using the substitution medthod   example of how it goes step by step

Suppose you are asked to solve the following system:

2x+3y=5
-3x+7y=11

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.)

2x+3y=5

2x=5-3y

`x=5/2-3/2y`

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.)

-3x+7y=11

`-3(5/2-3/2y)+7y=11`  ** Substituting in place of "x" **

`-15/2+9/2y+7y=11`

`-15/2+23/2y=11`

Notice that the new equation involves only one variable, so it is amenable to standard techniques.

`23/2y=22/2+15/2`

`y=2/23*22/2+2/23*15/2`

`y=22/23+15/23`

`y=37/23`

Then `x=5/2-3/2y` ==>`x=5/2-3/2(37/23)`

`x=5/2-111/46=2/23`

The solution will be `x=2/23,y=37/23`

Check: 2x+3y=5

`2(2/23)+3(37/23)=4/23+111/23=115/3=5`

-3x+7y=11

`-3(2/23)+7(37/23)=-6/23+259/23=253/23=11`

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