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.
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.
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,
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.
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.