Pair of linear equations in two variables — lesson. Mathematics CBSE, Class 10.

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A linear equation in which two variables are involved in which each variable is in the first degree.

It can be written in the form of

$ax + by + c = 0$ where

$a$ ,

$b$ , and

$c$ are real numbers, both

$a$ and

$b$ are not equal to zero,

$x$ and

$y$ are variables and

$c$ is a constant.

Example:

$2x + y = 8$ ,

$x - y - 1 = 0$ ,

$y = 2x$ are examples of linear equations in two variables.

We have also learnt about the solution of an equation.

A solution of an equation is a number substituted for an unknown variable which makes the equality in the equation true.

Example:

Consider the equation

$x + 3 = 2y - 1$ . Check whether

$x = 0$ and

$y = 2$ is the solution of the equation.

Solution:

Simplifying, we have:

$x - 2y = -4$

To verify whether

$x = 0$ and

$y = 2$ is the solution of the equation, let us substitute

$x = 0$ and

$y = 2$ in the given equation.

LHS

$= 0 - 2(2) = 0 - 4 = -4 =$ RHS

Therefore,

$x = 0$ and

$y = 2$ is the solution of the equation.

Geometrically, we can plot this point

$(0,2)$ on the line

$x + 3 = 2y - 1$ . This implies that every solution of the equation is a point on the line representing it.

Did you find an error?

2. Pair of linear equations in two variables