Choose two equations with the same X and Y unknowns. For example, use 2X + Y = 4 and X - Y = -1.
Select one of the equations and one unknown to solve. For example, use 2X + Y = 4 and solve Y.
Isolate Y on the left side of the equal sign using algebraic arithmetic to move all other terms to the right of the equal sign. Rewrite the first equation to look like Y = 4 - 2X.
Rewrite the second equation replacing Y with the equivalent expression from the right of the first equation to form an equation with X as the only unknown. The second equation now looks like X - (4 - 2X) = -1
Solve the new equation in Step 4 for the single unknown using standard algebraic methods. To solve the example, rewrite the equation to look like 3X = -1 + 4. Then solve 3X = 3 so X = 1.
Replace the value of X from Step 5 in the first equation in Step 3 to solve for Y. Write Y = 4 - 2(1) and solve to discover Y = 2.