Write the equations with one on top of the other. For example, if the equations are 3y + 2x = 5 and x - 5y = -17, then write them as
3y + 2x = 5
x - 5y = -17.
Rearrange the terms of the equations so that like terms match up. For the example, switch the first two terms in the first equation so that the x-terms and y-terms add up. So
3y + 2x = 5 becomes 2x + 3y = 5 and the two equations will read
2x + 3y = 5
x - 5y = -17.
Multiply an entire equation by a number to create a term that mirrors a term in the other equation. For the example, multiplying the second equation by -2 will make the x-term -2x and opposite from the x-term 2x in the other equation, resulting in
-2x + 10y = 34.
Combine the two equations together by addition. For the example, combining
2x + 3y = 5 and -2x + 10y = 34 results in 13y = 39. The 2x and -2x terms cancel each other out.
Solve for the remaining variable. For the example, 13y = 39 and y = 3.
Plug the variable into either starting equation. For the example, plugging y = 3 into x - 5y = -17 results in x - 15 =-17 and x = -2.