In general, what is a solution to a system of linear equations? Describe it both graphically and algebraically.
Graphically, it is the ordered pair where the lines intersect; algebraically, it is the
What would the graph of a system with no solution look like? Why?
It would be a pair of parallel lines; there would be no point of intersection, and the only way for this to happen is for the lines to be parallel.
What would the graph of a system with infinitely many solutions look like? Why?
It would be a single line that overlaps itself; if two equations result in the same line, all the points on the line are solutions to the system.
In Part 2, what is the goal of using elimination to solve the system?
Cancel out one variable to leave another equation with only one variable.
How could you eliminate
Answers vary. Possible answer: Multiply the bottom equation by
If you multiply the bottom equation by
If you know the
Substitute
How else could you have solved this system of equations by elimination?
Answers vary. Encourage students to think of at least two different ways to eliminate
ASSESS READINESS | MISCONCEPTIONS | WARM UP | FOCUS | EXTEND | FINISH |