Chapter 3 · Question 6

State the cross-multiplication formula for solving a pair of linear equations.

Answer Revealed

Direct Answer:

For

a_1x+b_1y+c_1=0

and

a_2x+b_2y+c_2=0

\frac{x}{b_1c_2-b_2c_1}=\frac{y}{c_1a_2-c_2a_1}=\frac{1}{a_1b_2-a_2b_1}

, provided

a_1b_2-a_2b_1\ne0

Cross-multiplication gives direct formulas for

x

and

y

when the pair has a unique solution.

The method is used when

a_1b_2-a_2b_1\ne0

. The formula is

\frac{x}{b_1c_2-b_2c_1}=\frac{y}{c_1a_2-c_2a_1}=\frac{1}{a_1b_2-a_2b_1}

. It is a compact algebraic way to solve a consistent pair with a unique solution.

For $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ , $\frac{x}{b_1c_2-b_2c_1}=\frac{y}{c_1a_2-c_2a_1}=\frac{1}{a_1b_2-a_2b_1}$ , provided $a_1b_2-a_2b_1\ne0$ .
Use the NCERT formula or theorem carefully.
Write units and final conclusion where applicable.

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