Question

How do you know theres a unique solution to simultaneous equations?

Answer 1

Answer:

Step-by-step explanation:

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.

Answer 2

Answer:

For a homogeneous system of equations ax+by=0 and cx+dy=0, the situation is slightly different. These lines pass through the origin. Thus, there is always at least one solution, the point (0,0). If the slopes -a/b and -c/d are equal then there are an infinite number of solutions since the lines are identical.