Equations having one variable and the degree of the variable being one is known as a linear equation in one variable. It can be represented by a line parallel to one specific axis. As the number of variables increases, it becomes a linear equation in two variables which becomes more complex. A linear equation in two variables is represented by a line in the cartesian plane varying according to the coefficients of the variable terms.
The standard form of a linear equation in two variables is represented as Where a and b are real numbers, and both a and b are not equal to zero. Every linear equation in one variable has a unique solution.
Both sides of the equation are supposed to be balanced for solving a linear equation. Equality sign denotes that the expressions on either side of the ‘equal to’ sign are equal. Since the equation is balanced, for solving it certain mathematical operations are performed on both sides of the equation in a manner that it does not affect the balance of the equation. For solving equations with variables on both sides, the following steps are followed:
Steps to simplify a linear equation in one variable:
For solving equations with variables on both sides, the following steps are followed:
Consider the equation: 5x – 9 = -3x + 19
Step 1: Transpose all the variables on one side of the equation. By transpose we mean to shift the variables from one side of the equation to the other side of the equation. In the method of transposition, the operation on the operand gets reversed.
In the equation 5x – 9 = -3x + 19, we transpose -3x from the left hand side to the right hand side of the equality, the operation gets reversed upon transposition and the equation becomes:
5x – 9 +3x = 19
⇒ 8x -9 = 19
Step 2: Similarly transpose all the constant terms on the other side of the equation as below:
8x -9 = 19
⇒ 8x = 19 + 9
⇒ 8x = 28
Step 3: Divide the equation with 8 on both sides of the equality.
8x/8 = 28/8
⇒ x = 28/8
If we substitute x = 28/8 in the equation 5x – 9 = -3x + 19, we will get 9 = 9, thereby satisfying the equality and giving us the required solution.
Click here to read about the application of linear equations.
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