Question

In linear equation, if you multiply the LHS by a number , then you should

(Choose)

*Divide the RHS by it

*Add it to RHS

*Multiply the RHS by it

*Subtract it from RHS

​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO CHOOSE THE CORRECT OPTION

In linear equation, if we multiply the LHS by a number , then we have to

• Divide the RHS by it

• Add it to RHS

• Multiply the RHS by it

• Subtract it from RHS

CONCEPT TO BE IMPLEMENTED

LINEAR EQUATION

A linear equation is an equation of first order.

Linear equation is defined as an algebraic equation in which each term has an exponent as one and the graphing of the equation results in a straight line.

CALCULATION

Let us consider a linear equation with one variable

$\sf{ax = b} \: \: .....(1)$

$\displaystyle \sf{ \: }Then \: \: \: x = \: \frac{b}{a}$

Now if we multiply the LHS by a number say c

$\sf{Then \: LHS \: becomes \: \: axc }$

Let k be the RHS after Multiplying LHS by c

So

$\sf{axc = k \: } \: \: ...(2)$

$\displaystyle \sf{ \: }Then \: \: \: x = \: \frac{b}{a} \: \: is\: the \: root \: of \: (2)$

$\implies \displaystyle \sf{ a \times \: \frac{b}{a} \times c = k }$

$\implies \displaystyle \sf{ k = bc }$

So RHS becomes bc

Hence we can conclude that In linear equation, if we multiply the LHS by a number , then we have to

Multiply the RHS by it

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Answer 2

Answer:

Linear Equations

Step-by-step explanation:

Let us take an equation x+2y=5 .....(1)

Put x=1 in eqn (1)

⇒y=2

So,x=1,y=2 is a solution of the equation

Multiplying both sides of equation 1() by 3, we get

3x+6y=15

Put x=1,y=2 in LHS

LHS =3×1+6×2=15= 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

⇒ 2x+y=25

​

Put x=1,y=2 in above equation

LHS = 21+2= 25

​

= RHS

Hence, on dividing or multiplying an equation by a non-zero number, the solution remains the same.

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