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Methods of Solving Systems of Linear Inequalities in Two Variables
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Substitution Method

To summarize, the following are the steps in solving a system of two linear equations in two variables using the substitution method:

Consider the system of equations,

{ A 1 x+ B 1 y= C 1 A 2 x+ B 2 y= C 2 .


Step 1.
 Using one of the two given equations, solve for one variable in terms of the other; that is, solve for y in terms of x, or solve for x in terms of y.

Step 2.
 Substitute the expression for y (or for x) that you obtained in step 1 in the other equation. Label the resulting equation as equation 1.

Step 3.
 Solve equation 1.

Step 4.
 Substitute the value of the variable you obtained in equation 1 in the expression you obtained in step 1. You will get the value of the other variable.

Step 5.
 Check the proposed solution by substituting the values of x and y in each given equation of the system.