# 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. There are two variables and both have unknown values.

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

IXL: Algebra 1: U.1 Is (x, y) a solution to the system 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: Number of solutions to a system of equations graphically (8th grade)

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

IXL: Algebra 1: U.2 Solve a system of equations by graphing

IXL: Algebra 1: U.3 Solve a system of equations by graphing: word problems

IXL: Algebra 1: U.4 Find the number of solutions to a system of equations by graphing

### 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: Systems of equations with substitution: y=4x-17.5 & y+2x=6.5 (one equation in slope-intercept form and one in standard; 8th grade)

Khan video: Systems of equations with substitution: 9x+3y=15 & y-x=5 (both in standard form; 8th grade)

Khan video: Systems of equations with substitution: 2y=x+7 & x=y-4 (both are in non-standard form; 8th grade)

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

IXL: Algebra 1: U.8 Solve a system of equations using substitution

IXL: Algebra 1: U.9 Solve a system of equations using substitution: word problems

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: 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

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

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

IXL: Algebra 1: U.10 Solve a system of equations using elimination

### 6.4 Solve System of Equations by Linear Combination (elimination): Word Problems

**Explanation**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**Khan exercise: Creating systems in context

Khan exercise: Systems of equations word problems

Khan exercise: Age word problems

IXL: Algebra 1: U.11 Solve a system of equations using elimination: word 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:****Practice Problems**Khan exercise: Number of solutions to a system of equations graphically (also in 6.1)

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

Khan exercise: Systems of equations word problems (with zero and infinite solutions)

IXL: Algebra 1: U.5 Find the number of solutions to a system of equations

### 6.7 Equivalent Systems of Equations (honors)

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

Khan video: Worked example: equivalent systems of equations

Khan video: Worked example: non-equivalent systems of equations

Khan video: Reasoning with systems of equations

Khan article: Equivalent systems of equations review

**Practice:**Khan Practice: Reasoning with systems of equations

### 6.8 System of Equations Mixed Review

**Practice Problems:**Jeopardy style-online game with system of equations - Reviews each method for solving system of equations

IXL: U.15 Solve a system of equations using any method: word problems

### 6.9 Inequalities with 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

IXL: Algebra 1: T.1 Does (x, y) satisfy the inequality?

IXL: Algebra 1: T.2 Linear inequalities: solve for y

IXL: Algebra 1: T.3 Graph a two-variable linear inequality

IXL: Algebra 1: T.4 Linear 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

IXL: Algebra 1: T.5 Is (x, y) a solution to the system of inequalities?

IXL: Algebra 1: T.6 Solve systems of linear inequalities by graphing

### 6.11 Linear Programming

**Explanation****Practice Problems**