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
$2 x - 3 y = 8; 4 x - 6 y = 9$

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Solution

$2 x - 3 y - 8 = 0 ⟶ (1)$
$4 x - 6 y - 9 = 0 ⟶ (2)$
$2 x - 3 y - 8 = 0$
Comparing with $a_{1} x + b_{1} y + c_{1} = 0$
$a_{1} = 2_{1} b_{1} = - 3_{1} c_{1} = - 8$

$4 x - b y - 9 = 0$
Comparing with $a_{2} x + b_{2} y + c_{2} = 0$
$a_{2} = 4 b_{2} = - 6 c_{2} = - 9$

$a_{1} = 2_{1} b_{1} = - 3_{1} c_{1} = - 8$
$a_{2} = 4 b_{2} = - 6 c_{2} = - 9$
$\frac{a_{1}}{a_{2}} = \frac{2}{4} = \frac{1}{2}$ $\frac{b_{1}}{b_{2}} = \frac{- 3}{- 6} = \frac{1}{2}$ $\frac{c_{1}}{c_{2}} = \frac{- 8}{- 9} = \frac{8}{9}$
Since, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
We have no solution,
Therefore, system of equation is inconsistent.

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Q. Question 3 (ii)
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.
2x - 3y = 8 ; 4x - 6y = 9

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

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

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On comparing the ratios a1a2,b1b2 and c1c2, find out whether the following pair of linear equations are consistent, or inconsistent2x−3y=8; 4x−6y=9

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
$2 x - 3 y = 8; 4 x - 6 y = 9$