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

Open in App

Solution

$3 x - 2 y - 5 = 0 ⟶ (1)$
$2 x - 3 y - 7 = 0 ⟶ (2)$
$3 x + 2 y - 5 = 0$
Comparing with $a_{1} x + b_{1} y + c_{1} = 0$
$a_{1} = 3, b_{1} = 2, c_{1} = - 5$

$2 x - 3 y - 7 = 0$
Comparing with $a_{2} x + b_{2} y + c_{2} = 0$
$a_{2} = 2, b_{2} = - 3, c_{2} = - 7$
$\frac{a_{1}}{a_{2}} = \frac{3}{2}, \frac{b_{1}}{b_{2}} = \frac{- 2}{3}, \frac{c_{1}}{c_{2}} = \frac{5}{7}$
Since, $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
We have a unique solution.
System of equation is consistant.

Suggest Corrections

Similar questions

Q. 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

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

Join BYJU'S Learning Program

On comparing the ratios a1a2,b1b2 and c1c2, find out whether the following pair of linear equations are consistent, or inconsistent3x+2y=5; 2x−3y=7

3x−2y−5=0⟶(1)2x−3y−7=0⟶(2)3x+2y−5=0Comparing with a1x+b1y+c1=0a1=3,b1=2,c1=−52x−3y−7=0Comparing with a2x+b2y+c2=0a2=2,b2=−3,c2=−7a1a2=32,b1b2=−23,c1c2=57Since, a1a2≠b1b2We have a unique solution.System of equation is consistant.

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