Question

Question 3 (ii)
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.
2x - 3y = 8 ; 4x - 6y = 9

Answer 1

The given equations are 2x - 3y = 8 and 4x - 6y = 9
They can be written as 2x - 3y -8 = 0 and 4x - 6y - 9 = 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:

$a_1=2,b_1=-3,and{c}_1=-8$
$a_2=4,b_2=-6and{c}_2=-9$

$\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{-3}{-6}=\frac{1}{2}$ and

$\frac{c_1}{c_2}=\frac{-8}{-9}=\frac{8}{9}$

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

Therefore, these linear equations represent parallel lines and thus have no possible solution.
Hence, the pair of linear equations is inconsistent.