Linear Equations Definition

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A linear equation is an equation in which the highest exponent of the variable is 1. A linear equation can consist of a single variable or more than one variable. The standard form of a linear equation with two variables ‘x’ and ‘y’ is represented as, Ax + By = C, where ‘A’, ‘B’ and ‘C’ are real numbers but ‘A’ and ‘B’ are not equal to 0. In order to find the value of the variable of the equation, we should solve the equation by performing some operations.
 
Example 1: Find the value of the variable ‘x’ in the given linear equation, x + 4 = 9.
Given linear equation: x + 4 = 9
In order to find the value of ‘x’, we first have to get rid of ‘4’ on its side.
This implies, subtract 4 on both sides of the equation.
This gives: x + 4 – 4 = 9 – 4.
So, x = 9 – 4 ==> x = 5.
Therefore the value of the variable ‘x’ in the given equation is 5.
 
Example 2: Find the value of the variable ‘b’ in the given linear equation, b – 3 = 10.
Given linear equation: b – 3 = 10
In order to find the value of ‘b’, we first have to get rid of ‘3’ on its side.
This implies, add 3 on both sides of the equation.
This gives: b – 3 + 3 = 10 + 3.
So, b = 10 + 3 ==> b = 13.
Therefore the value of the variable ‘b’ in the given equation is 13.


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