Question

The equations $4x+7y-10=0$ and $20x+35y-50=0$ are

• A. consistent and have a unique solution.
• B. consistent and have infinitely many solutions.
• C. inconsistent.
• D. None of these

Answer 1

The correct option is B consistent and have infinitely many solutions.

Given lines

$4x+7y-10=0$

$20x+35y-50=0\Rightarrow 4x+7y-10=0$

On comparing these equations with

$a_{1}x+b_{1}y+c_1=0\{a_1=4b_1=7c_1=-10\}{a}_{2}x+b_{2}y+c_2=0\{a_2=20b_2=35c_2=-50\}$

We know that here

$\frac{a_1}{a_2}=\frac{b_2}{b_2}=\frac{c^{}}{c_2}\frac{4}{20}=\frac{7}{35}=\frac{-10}{-50}=\frac{1}{5}$

We know that if $\frac{a_1}{a_2}=\frac{b_2}{b_2}=\frac{c_1}{c_2}$ this is the condition for infinitely many solutions .

Hence the equations have solutions therefore it is consistent.

Here both are same so they are consistent and because they are same they have many solutions .