System of Linear Equations - Practice Questions & MCQ

System of Linear Equation

1. System of 2 Linear Equations:

    It is a pair of linear equations in two variables. It is usually of the form

    Finding a solution for this system means to find the values of x and y that satisfy both the equations.

2. System of 3 Linear Equations:

    It is a group of 3 linear equations in three variables. It is usually of the form

    Finding a solution for this system means to find the values of x, y and z that satisfy all the three equations.

The system of equations are broadly classified into two types:

Consistent system of equations:

A system of equations is said to be consistent if it has at least one solution. Let the given system of equation is 

    E.g., x+ y = 2

            x - y = 6 is consistent because it has a solution x = 4 and y = -2.

Given lines are non-parallel, hence lines will have one point of intersection. 

In this case two lines represented by these lines coincide, so there are infinite pair of values of x and y that satisfy both the equations. This case is also counted as consistent as there is at least one solution.

Inconsistent equation:

A system of equations is said to be inconsistent if it has no solution.

For example, x+y = 5 and 2x+2y = 5 is inconsistent as it has no solution, just by seeing the equation, we get that it is the equation of two different parallel lines which never intersect. This lines are non-intersecting, hence there is no solution to this system.