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If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation

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changes

remains the same

changes in case of multiplication only

changes in case of division only

answer is B.

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Detailed Solution

It is given to find if the solution of linear equation changes after multiplying or dividing both sides with a non-zero number.
Let us take an equation

x + 2 y = 5

.....(1)
Put

x = 1

in eqn (1) ,

\Rightarrow (1) + 2 y = 5

\Rightarrow 2 y = 5 - 1

\Rightarrow 2 y = 4

Divide both the side by 2,

\Rightarrow y = 2

So,

x = 1, y = 2

is a solution of the equation.
Multiplying both sides of equation (1) by

3

, we get

\Rightarrow 3 (x) + 3 (2 y) = 3 (5)

\Rightarrow

3 x + 6 y = 15

Putting

x = 1, y = 2

in LHS
LHS

\Rightarrow 3 \times 1 + 6 \times 2

\Rightarrow 15

\Rightarrow LHS = RHS

Hence, on multiplying an equation by a non-zero number , the solution remains same.
Let us divide both sides of equation (1) by

2

\Rightarrow \frac{x}{2} + y = \frac{5}{2}

Put

x = 1, y = 2

in above equation.
LHS

\Rightarrow \frac{1}{2} + 2

\Rightarrow \frac{5}{2}

\Rightarrow

LHS=RHS
Hence, on dividing or multiplying an equation by a non-zero number, the solution remains the same.
Hence, option 2 is correct.

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