Question

Which of the following equations are consistent?

• A. $2x+4y=11;2x+4y=23$
• B. $7x-y=5;14x-2y=4$
• C. $x+y=7;2x-y=8$
• D. $x-y=5;2x-2y=11$

Answer 1

The correct option is C $x+y=7;2x-y=8$

Pair of equations is said to be consistent if they have at least one solution i.e., one or infinite solutions.
The pair of equations mentioned in options a, b and d has no solution as they are parallel lines. Pair of equations mentioned in c are:

$x+y=7...\left(i\right)$
$2x-y=8...\left(ii\right)$

Here, $a_1=1,b_1=1,c_1=7$
$a_2=2,b_2=-1,c_2=8$

$\Rightarrow \frac{1}{2}\ne \frac{1}{-1}$
$\therefore$ The pair of linear equations given in option c, is consistent and has a unique solution.