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If a system of linear equations has many solutions what would be the correct mathematical description of the system?
dependent
Solve this system of equations using the addition method x plus y equals 6?
When talking about a "system of equations", you would normally expect to have two or more equations. It is quite common to have as many equations as you have variables, so in this case you should have two equations.
When you solve a system of equations algebraically how can you tell whether the system has zero one or an infinite number of solutions?
Compare the equations. If it has the same slope it most likely will be parallel which means it has 0 solutions. However, if you plug in points and they match up exactly it would have an infinite amount of solutions. The only way it would intersect more than once or 2 then would be if it was a parabola which would have a x^2 value typically. If it has 1 solution it means it would intersect once.
Why are linear equations called linear equations?
Because, if plotted on a Cartesian plane, all solutions to the equation would lie on a straight line.
What would be a solution to a system?
The solution would be the point of intersection of the graphical representation of all equations within the system.
