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Question

Which of the following equation(s) is/are linear equation(s) in one variable?
I. 2x + 3y = 10
II. 4a + 3b = 3b + 6
III. 2x = 3x + 4

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Solution

If the degree of an equation is one, then that equation is called a linear equation. In all the equations given, the degree of each equation is one as the highest exponent of variables in a term is one.

Equations which have only one variable or which can be reduced to equations having only one variable are known as linear equations in one variable.

Since, 4a + 3b = 3b + 6 can be reduced to a linear equation in variable "a" by subtracting "3b" from both sides, this is a linear equation in one variable.

Also, 2x = 3x + 4 is a linear equation in one variable as it has only one variable, x.

The equation 2x + 3y = 10 is also linear but it has two variables, namely x and y. So, it is not a linear equation in one variable.

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