Solutions of a linear equation — lesson. Mathematics CBSE, Class 9.

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 + 2 y = 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 + 2 y = 20 \\ (2) + 2 (9) = 20 \\ 2 + 18 = 20 \\ 20 = 20 \end{array}

Here the solutions are \((0, 9)\) which are satisfy the

x + 2 y = 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 + 2 y = 20

equation, the result is not equal to \(20\) which is given in the equation.

\begin{array}{l} x + 2 y = 20 \\ (5) + 2 (10) = 20 \\ 5 + 25 = 20 \\ 25 \neq 20 \end{array}

Therefore \((5, 10)\) is cannot be the solution for the

x + 2 y = 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 + 2 y = 20

Step 1: Substitute \(x = 0\) in the given equation.

That is,

\begin{array}{l} x + 2 y = 20 \\ (0) + 2 y = 20 \\ 2 y = 20 \\ y = \frac{20}{2} \\ y = 10 \end{array}

Thus the value of (\(x, y)\) is \((0, 10)\) is the solution of

x + 2 y = 20

Similarly substitute \(y = 0\) in the equation

x + 2 y = 20

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

Therefore, the solution of the equation

x + 2 y = 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.

Previous theory

Exit to the topic

Next exercise

Send feedback

Did you find an error?

Send it to us!

2. Solutions of a linear equation

Theory: