If the coefficients of one of the variables in both equations are not additive inverses of each other or the exact same number, multiply or divide the equations by a constant so that one of the variable terms has the same or opposite coefficients.
Step III
Add or subtract equations in the system. This will result in one equation with a single variable.
Step IV
Solve the obtained equation with one variable.
Step V
Substitute the result into one of the equations to find the other variable.
Extra
Example
Consider the following system of linear equations.
4x+2y=5 & (I) 3x=2.5+y & (II)
Step I
In Equation (I), the variable terms are on the same side of the equation. However, in Equation (II) the variable terms are on both sides of the equations. We will first gather the variables on the left-hand side of the equation by Subtraction Property of Equality.
3x - y=2.5+y - y
⇕
3x-y=2.5
Step II
We will multiply both sides of Equation (II) by 2 to have opposite coefficients for the y-variable by using the Multiplication Property of Equality.
2 (3x-y)= 2(2.5)
⇕
6x-2y= 5
