Question

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

Answer 1

Finding the three different solutions to the equation:

The given equation is $x+2y=6$ …………$\left(i\right)$

By putting different values of $x$and $y$ we will find the solution of the equation.

Let $x=0$, and put the value in the equation $\left(i\right)$,we get;

$0+2y=6$.

$\Rightarrow 2y=6$

$\Rightarrow y=3$

Thus, $(0,3)$ is the first solution to the equation.

Let $y=0$, and put the value in the equation $\left(i\right)$,we get;

$x+2\left(0\right)=6$.

$\Rightarrow x+0=6$

$\Rightarrow x=6$
Thus $(6,0)$ is the second solution to the equation.

Now, let $x=2$, and put the value in equation $\left(i\right)$,we get;

$2+2y=6$.

$\Rightarrow 2y=6-2$

$\Rightarrow 2y=4$

$\Rightarrow y=2$

Thus, $(2,2)$ is the third solution to the equation.

Hence, $(0,3),(6,0)\&(2,2)$ are the three different solutions of $x+2y=6$.