5x+3y=2
2x+y=1

how to do it in the easy way?

solve one of them for X then feed that result into the other ;)

But that will make fractions arise. I suggest make 'y' the subject of formula for the second equation, then replace the function into the first equation.

5x+3y=2 / 2x+y=1 / how to do it in the easy way?
Just make one of the unknowns equal in quantity : lets make both

Multiply each item in ( 2x +y = 1 ) with 3 --> 6x + 3y = 3

Solve 3y --> 3y = 3 - 6x

Replace this into the first equation ( 5x + 3y = 2 ) ----> 5x + (3 - 6x) = 2

Solve : 5x + 3 - 6x = 2 ----> 5x - 6x = 2 -3 ----> -1x = -1 ----> x = 1

Fill that in in any of the equations and you'll find that y = -1

Simple, isn't it ?

:)