Question

Solve the following equations graphically :

`2 + (3y)/x = (6)/x`

`(6x)/y - 5 = (4)/y`

Answer 1

`2 + (3y)/x = (6)/x`

`(6x)/y - 5 = (4)/y`

`2 + (3y)/x = (6)/x` ⇒ 2x + 3y = 6  _________(1)

`(6x)/y - 5 = (4)/y` ⇒ 6x + 5y = 4  _________(2)

2x + 3y = 6 
⇒ y = `(6 - 2x)/(3)`
Corresponding values of x and y can be tabulated as :

x	3	-3	0
y	0	4	2

Plotting points (3, 0), (-3, 4), (0, 2) and joining them, we get a line l₁ which is the graph of equation (1).

6x - 5y = 4
⇒ y = `(6x - 4)/(5)`
Corresponding values of x and y can be tabulated as :

x	1	2	3
y	0.4	1.6	2.8

Plotting point (1, 0.4), (2, 1.6), (3, 2.8) and joining them, we get a line l₂ which is the graph of equation (2).

The line l₁ and l₂ intersect at a unique point `(3/2 ,1)`.