Question

Do the following equations represent a pair of coincident lines?

$-2x-3y=16y+4x=-2$

• A. No
• B. Yes
• C. Data Insufficient
• D. None of these

Answer 1

The correct option is A No

The given equations are

$-2x-3y=-2$ & $16y+4x=-2$

$⟹2x+3y+2=0$ and $4x+16y+2=0$

They are of the form $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0.$

Here, $a_1=2,a_2=4,b_1=3,b_2=16,c_1=2$ & $c_2=2.$

$\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2},\frac{b_1}{b_2}=\frac{3}{16}$ and $\frac{c_1}{c_2}=1$

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

We know that if there is a pair of equations like

$a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$, then the equations are consistent and coicident

If $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}.$

$\therefore$ They are not consistent & coincident equations.