Question

On comparing the ratios and , find out whether the following points of linear equations are consistent or inconsistent.

(i) 3x + 2y = 5, 2x – 3y = 7 (ii) 2x – 3y = 8, 4x – 6y = 9

Answer 1

We have,

(i) 3x + 2y = 5 3x + 2y – 5 = 0 and 2x – 3 y = 7 2x – 3y – 7 = 0

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

Here, $\frac{a_1}{a_2}$ ≠ $\frac{b_1}{b_2}$

Therefore, the given pair of linear equations is consistent.

(ii) 2x – 3 y = 8 Þ 2x – 3 y – 8 = 0 and 4x – 6 y = 9 Þ 4x – 6 y – 9 = 0

$\frac{a_1}{a_2}$ = $\frac{2}{4}$ = $\frac{1}{2}$ , $\frac{b_1}{b_2}$= $\frac{-3}{-6}$ = $\frac{1}{2}$ & $\frac{c_1}{c_2}$ = $\frac{-8}{-9}$

Here, $\frac{a_1}{a_2}$= $\frac{b_1}{b_2}$≠ $\frac{c_1}{c_2}$

Hence, the given pair is inconsistent