Find four different solutions of the equation x+2 y=6 - Vidyadip

Question

Find four different solutions of the equation $x+2 y=6$

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Answer

We have By inspection, $x=2, y=2$ is a solution because for $x=2, y=2 x+2 y=2+4=6$
Now, let us choose $x=0$. With this value of $x$, the given equation reduces to $2 y=6$ which has the unique solution $y=3$. So $x=0, y=3$ is also a solution of $x+2 y=6$.
Similarly, taking $y=0$, the given equation reduces to $x=6$. So, $x=6, y=0$ is a solution of $x+2 y=6$ as well. Finally, let us take $y=1$. The given equation now reduces to $x+2=6$, whose solution is given by $x=4$. Therefore, $(4,1)$ is also a solution of the given equation. So four of the infinitely many solutions of the given equation are: $(2,2),(0,3),(6,0)$ and $(4,1)$. Hence the required Solutions.

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