Line up the two equations vertically so that the x term, the y term and the constant line up. Then add to eliminate one variable. (If one variable doesn't eliminate multiply the entire equation by a number that will make one variable eliminate.) Solve the equation for the remaining variable. Substitute the answer back into one equation and solve for the other variable.
Examples:
x + 3y = 11 x  3y = 5 2x = 16 x = 8

2x + 5y = 5 x + 2y = 1 2x + 5y = 5 2x 4y = 2 (Equation 2 after being multiplied by 2) y = 3

Substitute into original equation. 

8 + 3y = 11 8 8 3y = 3 y = 1 
x + 2(3) = 1 x + 6 = 1 x =  5 





