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

2x - 3y = 8 ; 4x - 6y = 9
2x - 3y -8 = 0; 4x - 6y - 9 = 0
Comparing these equations with,
$a_{1}x+b_{1}y+c_1=0$
$a_{2}x+b_{2}y+c_2=0$
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
$\frac{c_1}{c_2}=\frac{8}{9}$
Hence, $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
Therefore, these linear equations are parallel to each other and thus have no possible solution.
Hence, the pair of linear equations is inconsistent.