What must be true of a linear system for it to have a unique solution? Select all that apply.

Solution:

Consider two linear equation is general as:

a₁x + b₁y + c₁= 0 and a₂x + b₂y + c₂ = 0.

This equation has unique solution if :

a₁ /a₂ ≠ b₁ /b₂.

In a set of linear simultaneous equations, a unique solution exists if and only if,

(a) the number of unknowns and the number of equations are equal,

(b) all equations are consistent, and

(c) there is no linear dependence between any two or more equations, that is,

all equations are independent.

What must be true of a linear system for it to have a unique solution? Select all that apply.

Summary:

Consider two linear equation is general as: a₁x + b₁y + c₁= 0 and a₂x + b₂y + c₂ = 0. A linear system for it to have a unique solution,a₁ /a₂ ≠ b₁ /b₂.