Question 3 (i)
On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ find out whether the following pair of linear equations are consistent, or inconsistent.
3x + 2y = 5 ; 2x - 3y = 7

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Solution

3x + 2y = 5 ; 2x - 3y = 7
3x + 2y - 5 = 0 ; 2x - 3y - 7 = 0
Comparing these equations with
$a_{1} x + b_{1} y + c_{1} = 0$
$a_{2} x + b_{2} y + c_{2} = 0$
We get
$a_{1} = 3, b_{1} = 2, a n d c_{1} = - 5$
$a_{2} = 2, b_{2} = - 3 a n d c_{2} = - 7$
$\frac{a_{1}}{a_{2}} = \frac{3}{2}$
$\frac{b_{1}}{b_{2}} = \frac{- 2}{3}$ and
$\frac{c_{1}}{c_{2}} = \frac{5}{7}$
Hence, $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
These linear equations are intersecting each other at one point and thus have only one possible solution. Hence, the pair of linear equations are consistent.

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Similar questions

Q. On comparing the ratios

\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}

and

\frac{c_{1}}{c_{2}}

, find out whether the following pair of linear equations are consistent, or inconsistent

3 x + 2 y = 5; 2 x - 3 y = 7

Question 3 (i)
On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ find out whether the following pairs of linear equations are consistent, or inconsistent.
3x + 2y = 5 ; 2x - 3y = 7

Question 3 (iv)
On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ find out whether the following pair of linear equations are consistent, or inconsistent.
5x - 3y= 11 ; -10x+ 6y= -22

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Question 3 (i) On comparing the ratios a1a2, b1b2 and c1c2 find out whether the following pair of linear equations are consistent, or inconsistent. 3x + 2y = 5 ; 2x - 3y = 7

Question 3 (i)
On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ find out whether the following pair of linear equations are consistent, or inconsistent.
3x + 2y = 5 ; 2x - 3y = 7