Question

Write the standard equation or general form of linear equation with two variables.

Answer 1

Hint: Linear equation represents a straight line. Linear equations in two variables makes it easy to explain the geometry of lines or the graph of two lines or equations. It contains two variables whose values are unknown.

Complete step-by-step answer:
The standard equation or general form of linear equation with two variables is-
$ \Rightarrow $ $ax + by = c$ Where a, b, c are real numbers while x and y are variables. Here, ‘a’ and b are not equal to zero.
Example- $4x + 3y = 10$ , $5x + y = 18$
It contains values of x and y both as a solution to make the two sides of the equation equal.
The linear equations of two variables are often used in following ways–
The problems can be solved by converting the situation into mathematical statements which tells the relation between the unknown variables. It makes it easier to solve such problems.
It is mainly used in linear programming problems called LPPs which involves analytical thinking and it deals with real life situations.

Note: There are infinitely many solutions for linear equations of two variables But to find the solution two equations should be given. There are three types of solutions-
Unique solution- The linear equations have unique solutions for both variables only if they both intersect at a single point. It means the slope formed by the two equations should not be equal.
No solution- The linear equations have no solutions if they do not intersect each other. This means they are parallel to each other and hence their slopes have equal value.
Infinite Solutions-The linear equations ${a_1}x + {b_1}y = {c_1}$ and ${a_2}x + {b_2}y = {c_2}$ have infinitely many solutions if and only if,
$\dfrac{{{a_1}}}{{{a_2}}} = \dfrac{{{b_1}}}{{{b_2}}} = \dfrac{{{c_1}}}{{{c_2}}}$
This means that the equations have slope in the same exact line.