Question

Solve graphically the following system of linear equations if it has unique solution:

2x - y = 9 

5x + 2y = 27

Answer 1

The given pair of linear equations is

2x – y = 9 or 2x – y – 9 = 0

and 5x + 2y = 27 or 5x + 2y – 27 = 0

On comparing the given equations with standard form of pair of linear equations i.e. a₁ x + b₁y + c₁ = 0 and a₂ x + b₂y + c₂ = 0, we get

a₁ = 2, b₁ = – 1 and c₁ = – 9

and a_{2 =} 5, b₂ = 2 and c₂ = – 27

The lines representing the given pair of linear equations will intersect at a point.

Here, the lines intersecting at point C i.e. (5,1)

Hence, the unique solution is x = 5 and y = 1.