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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
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.
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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