Number of Solutions of a System From Equations

Begin with the graphing sheet so students see parallel and matching lines. Then use the substitution sheet and finish with the equations sheet, which needs no graphing.

Rewrite twelve systems as y = mx + b and compare slopes and y-intercepts to count the solutions. The directions on the page read: Rewrite both equations as y = mx + b. Compare the slopes and the y-intercepts, then circle One, None or Many (infinitely many) solutions. An answer key is included.

Yes, both. We made it for 8th grade systems of equations, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

Write both equations as y = mx + b. Different slopes mean one solution. The same slope with different y-intercepts means no solution, and the same slope and y-intercept means infinitely many.

The variables cancel and you are left with a false statement, such as 0 = 5. A true statement, such as 4 = 4, means infinitely many solutions. Substitution With No or Infinitely Many Solutions practices both.

Both equations make the same line, so the two graphs lie on top of each other and share every point. Graph Systems, Parallel and Same Line Cases includes pairs like y = negative x + 4 and 2x + 2y = 8.