Question

How do you write a system of linear equations in two variables?

Answer 1

Hint: This type of question is based on the concept of linear equations. We need to first specify what a system of linear equations is and then we need to explain the concept of writing a system of linear equations in two variables.

Complete step by step answer:
For the given question, we define what is meant by a system of linear equations first. A system of linear equations is a set of equations that consists of 2 or more equations that have a common solution set. In this system, we can consider the equations as a representation of straight lines and a solution for this indicates the intersection point of these lines.
Now we define what a linear equation in two variables is. An equation is said to be a linear equation in two variables if it is represented in the form of $ax+by+c=0.$ Here the coefficients of x and y that is a and b are not equal to 0. Also, all the terms a, b and c are all real numbers.
We represent a system of linear equations in two variables, namely x and y, simply by varying the coefficients a, b and c.
For example,
$2x+3y-1=0......(1)$
$8x+12y-8=0......(2)$
These two above equations represent a set of two linear equations in two variables and these are obtained by setting $a=2,b=3,c=-1$ in the general equation to obtain equation (1) and $a=8,b=12,c=-8$ in the general equation to obtain equation (2).
Hence in conclusion, the general form for writing a system of linear equations in two variables is $ax+by+c=0.$

Note: We should have a proper knowledge in the topic of linear equations in order for us to clearly answer these types of questions. Care must be taken to ensure that the coefficients a and b are real numbers only.