# Systems of Equations and Inequalities

**What is a system of equations? **It is a collection of two or more equations with the same solution (common point) to both equations.

**When do we use a system of equations? **Typically, it used when there is more than one unknown quantity and you want a specific amount for each quantity.

For more information on the concept of a system of equations, click here.

**Determine if a point is a solution to a given system of equation**

**Explanation:**Khan video: Testing a solution for a system of equations

**Practice Problems:**Khan exercise: Solutions of systems of equations

**6.1 Solve system of equations by graphing**

**Explanation:**Khan video: Solving linear systems by graphing (both equations in slope-intercept form; 8th grade)

Khan video: Systems of equations with graphing: y=7/5x-5 & y=3/5x-1

Khan video: Graphing systems of equations (both equations are in standard form; 8th grade)

Khan video: Systems of equations with graphing: exact & approximate solutions

Khan video: Interpreting points in context of graphs of systems

**Practice Problems:**Khan exercise: Systems of equations with graphing

Khan exercise: Analyze the solutions of systems of equations graphically (8th grade)

Khan exercise: Interpret points relative to a system (honors)

**6.2 Solve system of equations by substitution**

**Explanation**Khan video: Systems of equations with substitution: -3x-4y=-2 & y=2x-5

Khan article: Substitution method review (systems of equations)

Khan video: Example 2: Solving systems by substitution (one equation in slope-intercept form and one in standard; 8th grade)

Khan video: Example 3: Solving systems by substitution (both equations in standard form; 8th grade)

Khan video: The substitution method (one standard form and one equation is x =; 8th grade)

**Practice Problems:**Khan exercise: Systems of equations with substitution

Worksheet: STEMersion

**6.3 Solve system of equations by linear combination (elimination)**

**Explanation**Khan article: Elimination method review (systems of linear equations)

Khan video: Systems of equations with elimination: x - 4y = -18 & -x + 3y = 11

Khan video: Systems of equations with elimination (and manipulation)

Khan video: Example 3: Solving systems by elimination (infinitely many solutions with graphing; 8th grade)

Khan video: Why can we subtract one equation from the other in a system of equations?

Khan video: Elimination strategies

**Practice Problems:**Khan exercise: Combining equations

Khan exercise: Elimination strategies (honors)

Khan exercise: Systems of equations with elimination - two coefficients are opposite

Khan exercise: Systems of equations with elimination challenge (honors only)

**6.4 Solve system of equations by linear combination (elimination): Word Problems**

**Explanation**Honors Notes | Annotated

Khan video: Systems of equations with elimination: Sum/difference of numbers (8th grade)

Khan video: Systems of equations with elimination: TV & DVD

Khan video: Systems of equations with elimination: apples and oranges

Khan video: Systems of equations with substitution: coins

Khan video: Systems of equations with elimination: coffee and croissants

Khan video: Setting up a system of linear equations example (weight and price)

Website article: Wind and Current Problems

**Practice Problems**

**6.5 Systems of Equations with three variables (honors)**

**Explanation****Practice:**

**6.6 State the Number of Solutions to a system of equations**

**Explanation:**Khan video: Number of solutions to a system of equations

Khan video: Number of solutions to a system of equations graphically

Khan video: Number of solutions to a system of equations algebraically

Khan article: Number of solutions to system of equations review

Khan video: Solving systems by graphing 3 (one equation in slope-intercept and the other needs to be changed; no solution; 8th grade)

Khan video: Solving systems by elimination 3 (and graphing; 8th grade)

Khan video: Solving systems by substitution 1 (and graphing; 8th grade)

Khan video: Example 1: Solving systems by substitution (no solution; 8th grade)

Khan video: Substitution method 2 (no solution; 8th grade)

**Practice Problems**

**6.7 Equivalent Systems of Equations (honors)**

**Explanation****Practice:**Khan Practice: Equivalent systems of equations (all content)

**6.8 System of Equations Mixed Review**

**Practice Problems:**Khan Practice - Systems of equations word problems capstone

Jeopardy style-online game with system of equations - Reviews each method for solving system of equations

**6.9 Graphing Inequalities in Two Variables**

**Explanation:**Khan Article: Graphing inequalities (x-y plane) review

Khan Video: Testing solutions to inequalities (verify solutions)

Khan Video: Intro to graphing two-variable inequalities (in slope-intercept form)

Khan Video: Graphing two-variable inequalities (in slope-intercept form)

Khan Video: Graphing inequalities 2 (in standard form) (old content)

Khan Video: Two-variable inequalities from their graphs (given a graph, find the inequality)

Khan video: Writing two-variable inequalities word problem

Khan video: Solving two-variable inequalities word problem

Khan video: Graphs of two-variable inequalities word problem

Khan video: Interpreting two-variable inequalities word problem

**Practice Problems**Khan Exercise: Solutions of inequalities: algebraic

Khan Exercise: Solutions of inequalities: graphical

Khan Exercise: Graphs of inequalities

Khan Exercise: Two-variable inequalities from their graphs

Khan Exercise: Two-variable inequalities word problems

Desmos Activity: Point Collector: Lines

**6.10 Systems of linear inequalities**

**Explanation:**Khan Video: Intro to graphing systems of inequalities

Khan video: Testing solutions to systems of inequalities

Khan Video: Graphing systems of inequalities (three inequalities)

Khan Video: Modeling with systems of inequalities (word problem)

Khan video: Writing systems of inequalities word problem

Khan video: Solving systems of inequalities word problem

Khan video: Graphs of systems of inequalities word problem

**Practice Problems:**Khan exercise: Solutions of systems of inequalities (testing points)

Khan exercise: Systems of inequalities graphs

Khan exercise: Systems of inequalities word problems

**Review**

**Practice Problems**