Question

Q.1 Tell which of the following is a linear equation in one variable:
a) x2 - 4x + 3 = 0
b) 6x – 2y = 7
c) 3x – 1 = -2x
d) pq - 3 =p
e) 3x + 2 = 4(x + 7) +9 ​

Answer 1

Answer:

option a , c and e

Step-by-step explanation:

Answer 2

Concept:

Linear equation in one variable:  An equation is said to be a linear equation in one variable if it contains only one variable and the highest exponent of this variable is 1. Linear equation in one variable is written as ax + b = 0.

Linear equation in two variables:  An equation is said to be a linear equation in two variables if it contains two variables and the highest exponent of these variables is 1. The linear equation in two variables is written as ax + by + c = 0.

Answer and explanation:

a) x² - 4x + 3 = 0

In the above-given equation, there is only one variable present but the highest exponent of that variable is here 2.

Hence, it is not a linear equation in one variable. It's a quadratic equation.

b) 6x - 2y = 7

In the above-given equation, there are two variables present, x and y.

The above equation can be written as,

6x - 2y - 7 = 0

It is of the form ax + by + c = 0.

Hence, it is a linear equation in two variables. It is not a linear equation in one variable.

c) 3x - 1= -2x

The above equation can be written as,

3x - 1 + 2x = 0

5x - 1 = 0

It is of the form ax + b = 0. It contains only one variable i.e. x.

Hence, it is a linear equation in one variable.

d) pq - 3 = p

The above-given equation contains two variables i.e., p and q.

Hence, it is not a linear equation in one variable.

e) 3x + 2 = 4(x + 7) +9 ​

3x + 2 = 4(x + 7) +9 ​

3x + 2 = 4x + 28 + 9

4x + 28 + 9 - 3x - 2 = 0

x + 35 = 0

It is of the form ax + b. It has only one variable i.e., x.

Hence, it is a linear equation in one variable.

Equations c) and e) are linear equations in one variable.

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