Question

Obtain the conditions of consistency and hence solve a given system of linear equations in two variables. (hint: show intersecting lines, parallel lines and coincident lines)​

Answer 1

Answer:

pair of linear equations in two variables have the same set of variables across both the equations. These equations are solved simultaneously to arrive at a solution. In this article, we will look at the various types of solutions of equations in two variables.

Suggested Videos

Play

Play

Play

Slider

Types of Linear Equations in Two Variables

Solutions of linear equations in two variables can be of three types

Single Solution

Infinite Solutions

No Solution

Understanding these types will help us in solving linear equations in two variables effectively. We will look at each of them in details.

Type 1: A single solution of a pair of linear equations in two variables

Consider the following pair of linear equations in two variables,

x – 2y = 0

3x + 4y = 20

The solution of this pair would be a pair (x, y). Let’s find the solution, geometrically. The tables for these equations are:

x 0 2

y = (1/2)x 0 1

x 0 4

y = (20 – 3x)/4 5 2

Now, take a graph paper and plot the following points:

A(0, 0)

B(2, 1)

P(0, 5)

Q(4, 2)

Next, draw the lines AB and PQ as shown below.

equations in two variables

From the figure above, you can see that the two lines intersect at the point Q (4, 2). Therefore, point Q lies on the lines represented by both the equations, x – 2y = 0 and 3x + 4y = 20. Hence, (4, 2) is the solution of this pair of equations in two variables. Let’s verify it algebraically:

x – 2y = 4 – 2(2) = 4 – 4 = 0 = RHS

3x + 4y = 3(4) + 4(2) = 12 + 8 = 20 = RHS

Further, from the graph, you can see that point Q is the only common point between the two lines. Hence, this pair of equations has a single solution.