Question

The following pair of linear equations consistent. State true and false:

$x+3y=11$; $2(2x+6y)=22$

• A. True
• B. False

Answer 1

The correct option is B False

The following pair of linear equation can be written as

$x+3y-11=0$ and $4x+12y-22=0$

Here, $a_1=1,b_1=3,c_1=-11$

And, $a_2=4,b_2=12,c_2=-22$

$\therefore \frac{a_1}{a_2}=\frac{1}{4}$ and $\frac{b_1}{b_2}=\frac{3}{12}=\frac{1}{4}$ and $\frac{c_1}{c_2}=\frac{-11}{-22}=\frac{1}{2}$

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

Thus, the given pair of linear equations are not consistent.