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

Consistent

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Inconsistent

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Ambiguous

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Data insufficient

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Solution

The correct option is B Consistent
The given linear equation are
$\Rightarrow 3 x + 2 y - 5 = 0$ ....(1)
$\Rightarrow a_{1} = 3, b_{1} = - 2, c_{1} = - 5$
$\Rightarrow 2 x - 3 y - 7 = 0$ .....(2)
$\Rightarrow a_{2} = 2, b_{2} = - 3, c_{2} = - 7$
$\Rightarrow \frac{a_{1}}{a_{2}} = \frac{3}{2}$
$\Rightarrow \frac{b_{1}}{b_{2}} = \frac{2}{- 3}$
$\Rightarrow \frac{c_{1}}{c_{2}} = \frac{- 5}{- 7}$
On comparing, we have
$\Rightarrow \frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}, \frac{c_{1}}{c_{2}}$
$\Rightarrow \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Hence, the following pair of equation is consistent.

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Similar questions

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 (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 pairs of linear equations are consistent, or inconsistent.3x+2y=5;2x−3y=7

The correct option is B ConsistentThe given linear equation are⇒3x+2y−5=0 ....(1)⇒a1=3,b1=−2,c1=−5⇒2x−3y−7=0 .....(2)⇒a2=2,b2=−3,c2=−7⇒a1a2=32⇒b1b2=2−3⇒c1c2=−5−7On comparing, we have⇒a1a2,b1b2,c1c2⇒a1a2≠b1b2Hence, the following pair of equation is consistent.

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