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# On comparing the ratios a 1 / a 2 , b 1 / b2 and c 1 / c 2, find out whether the lines representing the following pairs of linear equations are consistent, or inconsistent:: (iv) 5x - 3y = 11 ; -10x + 6y = -22

Q3.    On comparing the ratios $\frac{a_1}{a_2}$$\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing the following pairs of linear equations are consistent, or inconsistent:

(iv)    $5x - 3y = 11;\qquad -10x + 6y =-22$

Views

Given, Equations,

$5x - 3y = 11;\qquad \\-10x + 6y =-22$

Comparing these equations with  $a_1x+b_1y+c_1=0\:and\:a_2x+b_2y+c_2=0$, we get

$\\\frac{a_1}{a_2}=\frac{5}{-10}=-\frac{1}{2},\\\:\frac{b_1}{b_2}=\frac{-3}{6}=-\frac{1}{2}\:and\\\:\frac{c_1}{c_2}=\frac{11}{-22}=-\frac{1}{2}$

As we can see

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

It means the given equations have an infinite number of solutions and thus pair of linear equations is consistent.

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