Systems of Equations

Systems of equations are sets of multiple equations.  When you solve a system of equations, you find where those equations meet (points that both -- of all-- of the equations have in common). 

You can solve systems by graphing them and seeing where the graphs meet.  But, for more precision, it's best to use algebra to solve the systems (either substitution or elimination). 

There are three types of systems of linear equations, those with 1 solution, no solution, or infinite solutions.

All linear equations graph as lines.  A system of equations is more than one equation, so more than one line. The "solution" to that system of equations is where the lines cross.

Most lines intersect (or cross) once, so they have one solution, which is written as a coordinate. The solution of the system of lines graphed below is approximately (-3, -1)

If the two equations actually represent the same line (once you put the equations into $y=mx+b$ form, you should be able to see that they are identical), the system has infinite solutions. In the system below, the black line and the blue line are the same line, and both go on forever, so there are infinite solutions.

If the two equations represent parallel lines (you will see that they have the same slope), the system has no solutions. The lines below will never cross. The system below has no solutions.