If two linear mathematical expressions are connected and related by the sign of equality, an equation is formed. An equation satisfied for some particular value or values of the unknown quantity or quantities. The unknown quantity of an equation is called variable.
For example: - a x + b = c x + d
An equation containing one of the highest power of the unknown quantity is called a linear equation or first- degree equation.
a x + b = 0, a ≠ 0 is an example of linear equation.
How to solve a linear equation: -
Question 1: - Solve the linear equation 2 x + 4 = 8 and find the value of x.
Solution: -Step 1: - Try to keep all the variables on L.H.S. and constant on R.H.S.
Constant 4 is there on L.H.S., so we can subtract 4 from both sides to remove 4 from L.H.S., and then we get
2 x = 8 – 4
2 x = 4
Step 2: - Try to free the coefficients from the variable. So we will divide both sides by 2 so that coefficient of 2 will be remove from both sides.
2 x / 2 = 4 / 2
x = 2
Therefore x = 2
Question 2: - 6 x – 3 = 9, find x.
Solution: -6 x – 3 = 9
6 x = 9 + 3
6 x = 12
x = 12 / 6
x = 2