How do you tell if an equation has a unique solution?

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.

When linear equations has a unique solution lines are?

Answer: When a pair of linear equations has a unique solution lines are Intersecting.

Can a homogeneous system have a unique solution?

This is called the Trivial Solution. Since a homogeneous system always has a solution (the trivial solution), it can never be inconsistent. Thus a homogeneous system of equations always either has a unique solution or an infinite number of solutions.

What lines have infinite solutions?

Conditions for Infinite Solution If the two lines have the same y-intercept and the slope, they are actually in the same exact line. In other words, when the two lines are the same line, then the system should have infinite solutions.

What does it mean for an equation to have infinitely many solutions?

It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.

What is the condition of unique solution?

Condition for Unique Solution to Linear Equations A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point. i.e., if the two lines are neither parallel nor coincident.

What must be true for a linear system to have a unique solution?

What must be true of a linear system for it to have a unique​ solution? If the linear system is consistent and there is at least one free​ variable, the solution set contains infinitely many solutions. If the linear system is​ inconsistent, there is no solution.

How do you know whether an equation is an identity How many solutions does an identity have?

If solving a linear equation leads to a true statement such as 0 = 0, the equation is an identity. Its solution set is {all real numbers}. 2. If solving a linear equation leads to a single solution such as x = 3, the equation is conditional.

Can a homogeneous equation have a unique solution?

Since a homogeneous system always has a solution (the trivial solution), it can never be inconsistent. Thus a homogeneous system of equations always either has a unique solution or an infinite number of solutions. 1.

Can a homogeneous linear system have a unique solution?

A nxn homogeneous system of linear equations has a unique solution (the trivial solution) if and only if its determinant is non-zero. If this determinant is zero, then the system has an infinite number of solutions.