Question

$R$ is a relation on $N$ given by$R=\left\{(x,y):4x+3y=20\right\}$. Which of the following belongs to $R$?

• A. $(-4,12)$
• B. $(5,0)$
• C. $(3,4)$
• D. $(2,4)$

Answer 1

Answer: (A), (B), (D)

$(2,4)$

Explanation for the correct options:

Substituting $\left(2,4\right)$ in the given relation to see, if the relation is satisfied:

$4x+3y=20$

Substituting $x=2$

$$\begin{gathered} 8+3y=20 \\ \Rightarrow 3y=12 \\ \Rightarrow y=4 \end{gathered}$$

$x=(2,4)$ is the only ordered pair that satisfies the given relation.

Therefore, the correct answer is option (D).

Option (A): Substituting $\left(-4,12\right)$ in the given relation to see, if the relation is satisfied:

$4x+3y=20$

Substituting $x=-4$

$$\begin{gathered} -16+3y=20 \\ \Rightarrow 3y=36 \\ \Rightarrow y=12 \end{gathered}$$

$\left(-4,12\right)$ satisfies the relation .

Therefore, the correct answer is option (A).

Option (B): Substituting $\left(5,0\right)$ in the given relation to see, if the relation is satisfied:

$4x+3y=20$

Substituting $x=5$

$$\begin{gathered} 20+3y=20 \\ \Rightarrow 3y=0 \\ \Rightarrow y=0 \end{gathered}$$

$\left(5,0\right)$ satisfies the relation .

Therefore, the correct answer is option (B).

Explanation for the incorrect option:

Option (C): Substituting $\left(3,4\right)$ in the given relation to see, if the relation is satisfied:

$4x+3y=20$

Substituting $x=3$

$$\begin{gathered} 12+3y=20 \\ \Rightarrow 3y=8 \\ \Rightarrow y=\frac{8}{3} \end{gathered}$$

$\left(3,4\right)$ does not satisfy the relation.

Therefore, option (C) is the incorrect answer.

Therfore, the correct answers are option (A), (B), and (D).