Question

Determine whether the following lines are consistent or inconsistent:

$2x+y-6=0,4x-2y-4=0$

• A. The graph is coincident straight line.
• B. The graph is intersecting lines
• C. Inconsistent
• D. None of these

Answer 1

The correct option is B The graph is intersecting lines

Comparing $2x+y-6=0$ with $a_{1}x+b_{1}y+c_1=0$, we get, $a_1=2,b_1=1,c_1=-6$

and $4x-2y-4=0$ with $a_{2}x+b_{2}y+c_2=0$, we get$a_2=4,b_2=-2,c_2=-4$

Now

$\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{1}{-2}$

Here,

$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

$\therefore$ The equations are consistent and have exactly one solution. i.e the graph are intersecting lines.