Two Variables Equation

Two Variables Equation
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
two variables equation 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
two variables equation 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
two variables equation example
equations (3) and (4) are solutions of this group.
Removing Variable Using Substitution Method
Example
removing variable Using substitution method
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 Add and Subtract Method
Example
removing variable using add and subtract method
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.