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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Solution

5x - 3y = 11 ; -10x + 6y = -22
5x - 3y - 11 = 0 ; -10x + 6y + 22 = 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,
$a_{1} = 5, b_{1} = - 3, a n d c_{1} = - 11$
$a_{2} = - 10, b_{2} = 6 a n d c_{2} = 22$
$\frac{a_{1}}{a_{2}} = \frac{5}{- 10} = \frac{- 1}{2}$
$\frac{b_{1}}{b_{2}} = \frac{- 3}{6} = \frac{- 1}{2}$ and
$\frac{c_{1}}{c_{2}} = \frac{11}{- 22} = \frac{- 1}{2}$
Hence, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions.
Hence, the pair of linear equations is 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 pairs of linear equations are consistent, or inconsistent.

5 x - 3 y = 11; - 10 x + 6 y = 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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Question 3 (iv) On comparing the ratios a1a2, b1b2 and c1c2 find out whether the following pair of linear equations are consistent, or inconsistent. 5x - 3y= 11 ; -10x+ 6y= -22

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