Question

Graphically, the pair of equations $6x+3y+10=0$ and $2x+y+9=0$ represent two lines which are:

• A. intersecting at exactly one point.
• B. intersecting at exactly two points.
• C. coincident.
• D. parallel.

Answer 1

The correct option is D parallel.

The given lines are

$6x+3y+10=0$ and

$2x+y+9=0$

Now, we have

$a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$

and $\frac{a_1}{a_2}=\frac{b_1}{b_2}$, then the lines are parallel.

Here, $a_1=6,b_1=3,a_2=2,b_2=1$

$\therefore \frac{a_1}{a_2}=\frac{6}{2}=3$ and $\frac{b_1}{b_2}=\frac{3}{1}=3$

So, $\frac{a_1}{a_2}=\frac{b_1}{b_2}$.

Therefore, the given lines are parallel, i.e. there is no solution.