### Theory:

A solution means the value of an equation that satisfies the given equation.
In a two-variable equation, the solution also contains two values.

We use varies method to find the solution of a equation. Now we will see the two methods to find a solution of the equation.

Method I)

Consider a equation with two variable: $x+2y=20$.

As there are two variables in the equation, here the solution is a pair of values, one for $$x$$ and one for $$y$$ which satisfy the given equation.

In the above equation by inception if we substitute $$x = 2$$ and $$y = 9$$ we get the result $$20$$ as given in the equation.

$\begin{array}{l}x+2y=20\\ \\ \left(2\right)+2\left(9\right)=20\\ \\ 2+18=20\\ \\ 20=20\end{array}$

Here the solutions are $$(0, 9)$$ which are satisfy the $x+2y=20$ equation.

Here apart from the $$(0, 9)$$ the other values like $$(10, 5)$$ can also be a solution for the equation. We get the same answer by substituting as $$x = 10$$ and $$y = 5$$ in the given equation.

But on the other hand the values $$(5, 10)$$ is not the solution for the equation.

That is if we substitute $$x = 5$$ and $$y = 10$$ in the $x+2y=20$ equation, the result is not equal to $$20$$ which is given in the equation.

$\begin{array}{l}x+2y=20\\ \\ \left(5\right)+2\left(10\right)=20\\ \\ 5+25=20\\ \\ 25\ne 20\end{array}$

Therefore $$(5, 10)$$ is cannot be the solution for the $x+2y=20$ equation.

Method II)

Steps to find a solution of equation:
1. To find solution of a equation first substitute $$x = 0$$ and $$y = 0$$in the given equation.

2. Next perform an arithmetic operation to find the value of $$x$$ and $$y$$ which are the solution of given equation.
Consider a equation: $x+2y=20$.

Step 1: Substitute $$x = 0$$ in the given equation.

That is,

$\begin{array}{l}x+2y=20\\ \\ \left(0\right)+2y=20\\ \\ 2y=20\\ \\ y=\frac{20}{2}\\ \\ y=\phantom{\rule{0.147em}{0ex}}10\end{array}$

Thus the value of ($$x, y)$$ is $$(0, 10)$$ is the solution of $x+2y=20$.

Similarly substitute $$y = 0$$ in the equation $x+2y=20$.

$\begin{array}{l}x+2y=20\\ \\ x+2\left(0\right)=20\\ \\ x=20\end{array}$

Therefore, the solution of the equation $x+2y=20$ is $$(0$$,$$10)$$ and $$(20$$,$$0)$$.

Now we learned that, in a two variable equation the equation contain at least two solutions which are satisfy the equation.