Question

We know that coincident lines have infinite solutions so find out which among the following pairs of lines are coincident.

• A. $x-y=1$; $x+y=1$
• B. $3x=5+2y$; $y=4x+1$
• C. $x=\frac{11}{5}-\frac{2y}{5};y=\frac{11}{2}-\frac{5x}{2}$
• D. None of the above

Answer 1

The correct option is C

$x=\frac{11}{5}-\frac{2y}{5};y=\frac{11}{2}-\frac{5x}{2}$

After converting the given pairs of equations in the general form where
$a_{1}x+b_{1}y+c_1=0and{a}_{2}x+b_{2}y+c_2=0$,
it can be found that only for the pair
$x=\frac{11}{5}-\frac{2y}{5}andy=\frac{11}{2}-\frac{5x}{2},\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$,
which is the condition for coincident lines with infinite solutions.