Question

Following are three pairs of linear equations in two variables to show different Possibilities of

solutions graphically i.e
., unique solution, No solution and infinitely many solutions.

(a) 2x –y + 1 = 0 and x– 2y + 8 = 0

(b) x – 2y – 5 = 0 and 3x – 6y – 15 = 0

(c) 2x + 3y – 6 = 0 and 4x + 6y – 24 = 0
with graph
​

Answer 1

Answer:

Solution:

2x + 5y = 12

We have,

x + y = 3

When y = 0 we have x = 3

When x = 0 we have y = 3

Thus we have the following table giving points on the line x + y = 3

X 0 3

Y 3 0

Now, 2 + 5y = 12

When x = 1, we have

Thus we have the following table giving points on the line 2x + 5y = 12

X 1 -4

Y 2 4

Graph of the equation x + y = 3 and 2x + 5y = 12 is

Graph of the equation

Clearly two lines intersect at a point P (1, 2)

Hence x = 1 and y = 2