Solving for Both X and Y

Solving for two variables (normally denoted as “x” and “y”) requires two sets of equations. Assuming you have two equations, the best way for solving for both variables is to use the substitution method, which involves solving for one variable as far as possible, then plugging it back in to the other equation. Knowing how to solve a system of equations with two variables is important for several areas, including trying to find the coordinate for points on a graph.

Step 1

Write out the two equations that have the two variables you want to solve. For this example, we will find the value for “x” and “y” in the two equations “3x + y = 2” and “x + 5y = 20”

Step 2

Solve for one of the variables in on one of the equations. For this example, let’s solve for “y” in the first equation. Subtract 3x from each side to get “y = 2 – 3x”

Step 3

Plug in the y value found from the first equation in to the second equation in order to find the x value. In the previous example, this means the second equation becomes “x + 5(2- 3x) = 20”

Step 4

Solve for x. The example equation becomes “x + 10 – 15x = 20,” which is then “-14 x + 10 = 20.” Subtract 10 from each side, divide by 14 and you have end up with x = -10/14, which simplifies to x = -5/7.

Step 5

Plug in the x value in to the first equation to find out the y value. y = 2 – 3(-5/7) becomes 2 + 15/7, which is 29/7.

Step 6

Check your work by plugging in the x and y values in to both of the equations.