Are the following pair of linear equations consistent? Justify your answer.
$x + 3y = 11$
$2(2x + 6y) = 22$

(B) pair of linear equations is consistent if it has at least one solution. This occurs when:
$1$. $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$ (Unique solution)
$2$. $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$ (Infinitely many solutions)
Given equations:
$x + 3y = 11$ (Equation $1$)
$2(2x + 6y) = 22 \implies 4x + 12y = 22 \implies 2x + 6y = 11$ (Equation $2$)
Comparing with $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$:
For Equation $1$: $a_1 = 1, b_1 = 3, c_1 = -11$
For Equation $2$: $a_2 = 2, b_2 = 6, c_2 = -11$
Calculating ratios:
$\frac{a_1}{a_2} = \frac{1}{2}$
$\frac{b_1}{b_2} = \frac{3}{6} = \frac{1}{2}$
$\frac{c_1}{c_2} = \frac{-11}{-11} = 1$
Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$,the lines are parallel and have no solution.
Therefore,the given pair of linear equations is inconsistent.