Question

Graphically, the pair of equations $6x-3y+10=0;2x-y+9=0$ represents 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.

Step 1: Evaluate the first equation

The given equation is $6x-3y+10=0$.

Assuming various values of $x$ and $y$ we get the following table:

$x$	$0$	$-\frac{5}{3}$
$y$	$\frac{10}{3}$	$0$

Step 2: Evaluate the second equation

The given equation is $2x-y+9=0$.

Assuming various values of $x$ and $y$ we get the following table:

$x$	$0$	$-\frac{9}{2}$
$y$	$9$	$0$

Step 3: Plotting the graph:

Hence, from the diagram, we can see that the two given lines are parallel to each other.

Therefore, option $\left(D\right)$ is the correct answer.