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

3x + 2y = 14

x — 4y = — 14

The given pair of linear equations is

3x + 2y = 14 or 3x + 2y – 14 = 0

and x – 4y = – 14 or x – 4y + 14 = 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 = 3, b₁ = 2 and c₁ = – 14

and a_{2 =} 1, b₂ = – 4 and c₂ = 14

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 B i.e. (2,4)

Hence, the unique solution is x = 2 and y = 4.