# Systems of equations

Grade 10s are working on solving systems of equations. We’ve looked at using substitution and elimination to solve problems within a context. Today we looked at equations out of context, and we made the connection that the solution that is the end result of elimination or substitution represents the intersection of the two linear equations.

Most linear equations will intersect once, and that point can be found by substitution, elimination or graphing (desmos makes it really quick to find).

Some systems will not be easy to solve. Some will end up with an equation like 0=0 at the end. Others will end up with something like 0=5.

In the case of the first, 0=0, we know that is true, so it’s like the math says…yes. As in every point is a solution. When two lines are identical we have that case.

When we see something like 0=5 that is not true, so it’s like the math says…no. As in there is no solution. This means the lines are parallel and do not intersect.