Question

Graphically, the pair of equations

$\begin{array}{rcl}6x-3y+10& =& 0\\ 2x-y+9& =& 0\end{array}$

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: Finding the approach to solve the problem

• Notice that if we take 3 as common from equation (1), then the coefficients of $x\mathrm{and}y$ will be the same. It is known that two lines $l_{1}and{l}_2$ are parallel if they are in a form of $ax+by=c$ and $ax+by=d$.
• Here, $a,b,c\mathrm{and}d$ are constant.
• Therefore, we can check whether the given equations satisfy the condition to be parallel to each other.

Given two equation are as follows:

$\begin{array}{rcl}6x-3y+10& =& 0...\left(1\right)\\ 2x-y+9& =& 0...\left(2\right)\end{array}$

Step 2: Checking whether the equations are parallel or not

Take 3 as common from equation (1):

$$\begin{gathered} \therefore 3\left(2x-y+\frac{10}{3}\right)=0 \\ \Rightarrow 2x-y+\frac{10}{3}=0 \\ \Rightarrow 2x-y=-\frac{10}{3} \end{gathered}$$

Similarly, rewrite the equation (2) as follows:

$2x-y=-9$

Clearly, given equations are parallel as they fulfill the necessary condition to be parallel.

Final Answer: Hence, option D is correct.