### 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.
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.