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

3y = 5 — x

2x = y + 3

The given pair of linear equations is

x + 3y = 5 or x + 3y – 5 = 0

and 2x – y = 3 or 2x – y – 3 = 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 = 1, b₁ = 3 and c₁ = – 5

and a_{2 =} 2, b₂ = – 1 and c₂ = – 3

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

Now, table for or

Now, table for or

Here, the lines intersecting at point C i.e. (2,1)

Hence, the unique solution is x = 2 and y = 1.