Question

Graphically, solve the following pair of equations:

2x + y = 6, 2x – y + 2 = 0

Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.

Answer 1

Given equations are 2x + y = 6 and 2x – y + 2 = 0

Table for equation 2x + y – 6 = 0

For x = 0, y = 6

For y = 0, x = 3

x	0	3
y	6	0

Table for equation 2x – y + 2 = 0

For x = 0, y = 2

For y = 0, x = –1

x	0	–1
y	2	0

Let A₁ and A₂ represent the areas of triangles ACE and BDE respectively.

Let, Area of triangle formed with x-axis = A₁

A₁ = Area of ΔACE

= `1/2` × AC × PE

A₁ = `1/2` × 4 × 4

= 8

And Area of triangle formed with y-axis = A₂

A₂ = Area of ΔBDE

= `1/2` × BD × QE

A₂ = `1/2` × 4 × 1

= 2

A₁:A₂ = 8:2 = 4:1

Hence, the pair of equations intersect graphically at point E(1, 4) i.e., x = 1 and y = 4.