Question

Interpretation of the pair of equations (Table with Diagram)​

Answer 1

Step-by-step explanation:

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.