### Theory:

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.

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**.