Name: Cross Multiplication Method: Illustration
Uploaded: 2019-07-19
Duration: 7 min 27 s
Description: This tutorial will show you many examples of solving linear equations in two variables using the cross-multiplication method with a clear step-by-step explan...

Question

Given below are three equations. Two of them have infinite solutions and two have a unique solution. State the two pairs.

$3 x - 2 y = 4$

$9 x - 6 y = 12$

$6 x + 2 y = 4$

Accepted Answer

The given system of equations is

$3 x - 2 y - 4 = 0 . . . . (i)$

$9 x - 6 y - 12 = 0 . . . . (ii)$

$6 x + 2 y - 4 = 0 . . . . (iii)$

The standard form of a pair of linear equations is

$a_{1} x + b_{1} y + c_{1} = 0$

$a_{2} x + b_{2} y + c_{2} = 0$

Compare the equations $(i), (ii)$ with their standard forms, we get,

$\frac{a_{1}}{a_{2}} = \frac{3}{9} = \frac{1}{3}, \frac{b_{1}}{b_{2}} = \frac{- 2}{- 6} = \frac{1}{3}, \frac{c_{1}}{c_{2}} = \frac{- 4}{- 12} = \frac{1}{3}$

We observe that,

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

Hence, $3 x - 2 y = 4$ and $9 x - 6 y = 12$ have infinite solutions.

Now comparing equations $(i), (iii)$ with standard forms, we get,

$\frac{a_{1}}{a_{2}} = \frac{3}{6} = \frac{1}{2}, \frac{b_{1}}{b_{2}} = \frac{- 2}{2} = \frac{- 1}{1}, \frac{c_{1}}{c_{2}} = \frac{- 4}{- 4} = \frac{1}{1}$

Here, we observe that,

$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

Hence, $3 x - 2 y = 4$ and $6 x + 2 y = 4$ have unique solutions.

Given below are three equations. Two of them have infinite solutions and two have a unique solution. State the two pairs.

$3 x - 2 y = 4$

$9 x - 6 y = 12$

$6 x + 2 y = 4$

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

Given below are three equations. Two of them have infinite solutions and two have a unique solution. State the two pairs. 3x-2y=4 9x-6y=12 6x+2y=4

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

Given below are three equations. Two of them have infinite solutions and two have a unique solution. State the two pairs.

$3 x - 2 y = 4$

$9 x - 6 y = 12$

$6 x + 2 y = 4$