Question

Does the pair of the linear equation have
no solution ? Justite your answer.
3x + y - 3=0, 2x + 2/3y=2
​

Answer 1

Answer :-

No! The pair has infinite number of solutions.

Explanation -

$\sf 3x + y - 3 = 0$

➩ $\sf 3x + y = 3\: \: \: \: \: -i$

➩ $\sf 2x + \frac{2}{3} y = 2 \: \: \: \: \: -ii$

So, for the following equations -

• $\sf a_1 = 3$
• $\sf a_2 = 1$
• $\sf a_3 = 3$
• $\sf b_1 = 2$
• $\sf b_2 = \frac{2}{3}$
• $\sf b_3 = 2$

➩ $\sf \frac{a_1}{b_1} = \frac{3}{2}$

➩ $\sf \frac{a_2}{b_2} = \frac{1}{\frac{2}{3}} = \frac{3}{2}$

➩ $\sf \frac{a_3}{b_3} = \frac{3}{2}$

Here,

➩ $\sf \frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3}$

Hence, the equations have infinite number of solutions.