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.

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

Let, Area of triangle formed with x -axis = T₁

T₁ = Area of △ACE = ½ × AC × PE

T₁ = ½ × 4 × 4 = 8

And Area of triangle formed with y – axis = T₂

T₁ = Area of △BDE = ½ × BD × QE

T₁ = ½ × 4 × 1 = 2

T₁:T₂ = 8:2 = 4:1

Hence, the pair of equations intersect graphically at point E(1,4)

i.e., x = 1 and y = 4.