Two Variable Equations

If there are two unknown variables in an equation, and the degree of unknown variable is one, then this equation is called two variables one degree equation. Example.

Example

equation (1) has variables x and y, both are one degree, then equation (1) is called two variables one degree equation.

Group of Two Variables Equation

The group is constructed by two independent equations, each of them is two variable one degree equation. The number of equations in the group is equal to the number of variables in the group.

Example

equations (1) and (2) are within a group, both are independent.

Solution of Two Variables Equation

In the group of two variables one degree equation, the values of the unknown variables which make the left side of the equation is equal to the right side of the equation is called the solution.

Example

equations (3) and (4) are solutions of this group.

Removing Variable Using Substitution Method

Example

Steps using substitution method: Step 1: Change equation (1) to express variable x in terms of y, such that, x = 3 - 2y , which is equation (3).; Step 2: Substitute equation (2) for equation (3) to remove the variable x.; Step 3: Solve this one variable equation, we get y = 1.; Step 4: Substitute equation (3) for the value of y to get the value of x.

Removing Variable Using Addition and Subtraction Method

Example

Steps using add-subtraction method: Step 1: In order to remove second terms in both equations, we multiply two to each term in equation (2), that is 6x - 2y = 4, this is equation (3).; Step 2: Add equation (3) and equation (1) to remove variable y, we have the equation 7x = 7.; Step 3: Solve this equation, we get x = 1.; Step 4: Substitute equation (2) for the value of x to get the value of y.