Determine which variable to solve first. If you are asked to solve more than one variable at one time, such as x and y, then you will be given a set of equations. Sample equations are 3x + y + 2/3 = 0 and x + 2y + 5/3 = 0. The variables are x and y, and you may decide to solve x first.
Solve the first equation for the variable y so that y is on the left side of the equation and the terms containing x and the fractions and numbers are on the right side of the equation. Beginning with the first equation, the process is:
3x + y + 2/3 = 0
y = - 3x - 2/3
The expression - 3x - 2/3 is now a substitute for y.
Substitute the expression -3x - 2/3 for y in the second equation, and solve x. The process is:
x + 2y + 5/3 = 0 (second equation)
x + 2(-3x - 2/3) + 5/3 = 0
x -6x - 4/3 + 5/3 = 0
-5x + 1/3 = 0
-5x = -1/3
x = 1/15
Substitute the value of 1/15 for x in one of the equations. For example, you could choose the equation already solved for y:
y = -3x - 2/3
y = -3(1/15) - 2/3
y = 15(-3/15 - 2/3)
y = -3 -10
y = -13
Report the solution for x and y as a solution set: { x = 1/15, y = -13 }