What is the difference between an equation and systems of equations?

Question

Do all systems have solutions? Explain or provide an example.

Answer 1

An system of equations is a group of equations that relate to each other.  For a system of equations to have a single solution, there must be at least as many equations as variables.

Typically, a system of equations will have only one solution, if there are as many equations as variables.  If the variables are raised to a power greater than one, there could be more than one solution.

If two of the equations in a system are the same equation, but written differently, the equation will have infinite solutions.  For example 2x - y = 4 and y = 2x + 4 would produce an infinite number of solutions.

It is possible for a system of equations to have no solution.  For example, parallel lines never intersect, so there is no solution (2x + 1 = 0 and 2x + 1 = 2).