Question

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

Answer 1

The given equations are 3x + 2y = 5 and 2x - 3y = 7.
They can be written as 3x + 2y - 5 = 0 and 2x - 3y - 7 = 0

Comparing these equations with $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$, we get

$a_1=3,b_1=2,and{c}_1=-5$
$a_2=2,b_2=-3and{c}_2=-7$

$\frac{a_1}{a_2}=\frac{3}{2}$
$\frac{b_1}{b_2}=\frac{-2}{3}$ and
$\frac{c_1}{c_2}=\frac{5}{7}$

Hence, $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

These linear equations represent a pair of intersecting lines, and can have one possible solution.

Hence, the pair of linear equations is consistent.