Math 1B‎ > ‎

Unit 7

Systems of Equations & Inequalities

Unit Description

    In this unit, students will apply their knowledge of solving linear equations to solving systems of two linear equations. Students will learn to solve systems of equations using several methods (tables, graphs, substitution, and elimination) They will decide which method is most efficient for the given problem, as well as decide whether the answer should be exact or approximate. . Students will continue the study of systems of equations by answering questions that require the interpretation and justification of the solution in real-life application problems. Students deepen their understanding of inequalities by looking at systems of inequalities. Students will also investigate the slope criteria for parallel and perpendicular lines and use it to write equations of parallel and perpendicular lines and complete simple coordinate geometry proofs. Students will find the midpoint of a segment.

Unit Skills 
  1. By the end of the unit, students will be able to:
  2. Solve systems of linear equations exactly. (Solve systems of two linear equations in two variables algebraically.)
  3. Solve simple cases of systems of equations by inspection.
  4. Solve systems of linear equations approximately using technology to graph the functions. (Estimate solutions by graphing the equations.)
  5. Solve systems of linear equations approximately by making tables of values or finding successive approximations.
  6. Solve real-world and mathematical problems leading to two linear equations in two variables.
  7. Choose and interpret the scale and the origin in graphs and data displays.
  8. Create equations in two or more variables to represent relationships between quantities.
  9. Graph equations on coordinate axes with labels and scales.
  10. Represent constraints by systems of linear equations and/or inequalities.
  11. Interpret solutions to systems of linear equations/inequalities as viable or non-viable options in a modeling context.
  12. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
  13. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x).
  14. Graph the solutions to a linear inequality in two variables as a half- plane (excluding the boundary in the case of a strict inequality).
  15. Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
  16. Use coordinates to prove simple geometric theorems algebraically (e.g. prove that a quadrilateral created by connecting four points is a parallelogram using the slope criteria and/or distance on the coordinate plane).
  17. Prove the slope criteria for parallel and perpendicular lines.
  18. Use the slope criteria to solve geometric problems (e.g., determine if two lines are parallel, perpendicular, or neither; find the equation of a line parallel or perpendicular to a given line that passes through a given point; find the coordinates of a fourth vertex of a quadrilateral given three vertices and its shape).
  19. Find the midpoint of a segment.


Vocab & Concept Review

Khan Academy Practice:

  Unit 7 Part 1
Midpoint Stations Links:

Unit 7 Part 2

  • Socrative Quiz 
    • (follow link, enter room # 3QVJ3WLV aand your 1st name last initial, then take short quiz)