Math 1 · Unit 6
Systems of Equations and Inequalities
Six lessons: what a system is and solving by graphing, substitution, elimination, how many solutions, systems of inequalities, and systems in the real world. A solution has to work in every equation, or land in every region. Each card below opens a lesson. Every lesson has practice with hints, a study guide, a worksheet with an answer key, and a lesson plan.
What a System Is, and Solving by Graphing
A system is two equations at once, and a solution has to work in every one of them: on a graph, the point where the lines cross. Graph both from m and b, read the crossing, check it in both equations, and see why exact answers need algebra.
Start Unit 6, Lesson 1Solving by Substitution
If one equation says what y equals, put that expression in for y in the other equation. Two variables become one, and it is a Unit 1 equation. Back-substitute, check the pair in both, and get exact answers even when the graph could only estimate.
Start Unit 6, Lesson 2Solving by Elimination
Line the equations up and add them so one variable cancels, using opposite coefficients that add to zero: the make-a-zero-appear idea from Unit 1. Multiply one or both equations first when you need to. Then a note on choosing the easiest method.
Start Unit 6, Lesson 3How Many Solutions?
Different slopes cross once. Parallel lines never meet, and the algebra ends in a false line. The same line twice meets everywhere, and the algebra ends in a true line. Compare m and b to predict the number of solutions before solving, then confirm.
Start Unit 6, Lesson 4Systems of Inequalities
Two inequalities at once: shade each one the Unit 5 way, in its own color, and the solution is the overlap, the region shaded by both. Test a point in both inequalities to see whether it is in the overlap.
Start Unit 6, Lesson 5Systems in the Real World
Two facts about two unknowns, such as a total count and a total value, become two equations to solve and read back into the story. Two limits, such as a budget and a time limit, become two inequalities whose overlap is every plan that obeys both, with whole-number plans as dots.
Start Unit 6, Lesson 6Printables for Unit 6
Study guides, worksheets with answer keys, and lesson plans for every lesson in this unit.