Question

Find the solution of the equation $x+2y=6$ from the options given below:

• A. $(0,3),(6,0),(2,2)$ and $(4,1)$
  
• B. $(0,2),(6,0),(2,2)$ and $(4,1)$
  
• C. $(0,3),(6,0),(2,2)$ and $(3,1)$
  
• D. $(0,3),(6,0),(1,2)$ and $(4,1)$
  

Answer 1

Answer: (A)

$(0,3),(6,0),(2,2)$ and $(4,1)$

The given equation is $x+2y=6$ .....(1)
Putting $x=0$ in equation 1, we get
$\Rightarrow 0+2y=6$
$\Rightarrow 2y=6\Rightarrow y=3$
$(0,3)$ is a solution
Putting $y=0$ in equation 1, we get
$\Rightarrow x+2\times 0=6$
$\Rightarrow x=6$
$(6,0)$ is a solution.
Putting $x=2$ in equation 1, we get
$\Rightarrow 2+2y=6$
$\Rightarrow 2y=6-2\Rightarrow 2y=4$
$\Rightarrow y=2$
$(2,2)$ is a solution.
Putting $x=4$ in equation 1, we get
$\Rightarrow 4+2y=6$
$\Rightarrow 2y=2\Rightarrow y=1$
$(4,1)$ is a solution.
Hence, $(0,3),(6,0),(2,2)$ and $(4,1)$ are four solutions of given equation.