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.
$x - 3 y = 4; 3 x + 2 y = 1$

consistent

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

inconsistent

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Ambiguous

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A consistent
The equations are
$x - 3 y - 4 = 0$
$\Rightarrow a_{1} = 1, b_{1} = - 3, c_{1} = - 4$
$3 x + 2 y - 1 = 0$
$\Rightarrow a_{2} = 3, b_{2} = 2, c_{2} = - 1$
comparing $\frac{a_{1}}{a_{2}} a n d \frac{b_{1}}{b_{2}}$
We have $\frac{1}{3} \neq \frac{- 3}{2}$
$\Rightarrow \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
$\Rightarrow S y s t e m h a s u n i q u e s o l u t i o n$
If the system has unique solution then it is said to be consistent system

Suggest Corrections

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 pair of linear equations are consistent, or inconsistent

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

Q. 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

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 inconsistent.x−3y=4;3x+2y=1

The correct option is A consistentThe equations are x−3y−4=0⇒a1=1,b1=−3,c1=−4 3x+2y−1=0⇒a2=3,b2=2,c2=−1 comparing a1a2andb1b2We have 13≠−32⇒a1a2≠b1b2⇒System has unique solutionIf the system has unique solution then it is said to be consistent system

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.
$x - 3 y = 4; 3 x + 2 y = 1$