Systems of Equations and Systems of Inequalities

Substitution

100

Solve the system using substitution:

y=x+2

x+y=8

Give answer as a point (ex (0,0))

(3,5)

200

Solve the system using substitution:

y=2x-1

3x+y=11

Give answer as a point (ex (0,0))

(3,5)

300

Solve the system using substitution:
x=2y+1

3x-2y=18

Give answer as a point (ex (0,0))

(5,2)

400

Solve the system using substitution:

2x+3y=7

x=4-2y

Give answer as a point (ex (0,0))

(1,3/2) or (1,1.5)

500

Solve the system using substitution:

y=3/2x-4

4x-2y=23

Give answer as a point (ex (0,0))

Express in fractional form

(31/5, 53/10)

Elimination

100

Solve the system using elimination: 

x+y=6

x-y=2

Give answer as a point (ex (0,0))

(4,2)

200

Solve the system using elimination:

2x+y=10

2x-y=2

Give answer as a point (ex (0,0))

(3,4)

300

Solve the system using elimination:

3x+2y=14

3x-2y=2

Give answer as a point (ex (0,0))

(8/3,3) or (2.67,3)

400

Solve the system using elimination:

2x+3y=7

4x+6y=20

Give answer as a point (ex (0,0))

No solution

500

Solve the system using elimination:

3x-2y=4

5x+4y=22

Give answer as a point (ex (0,0))

Express in fractional form

(30/11, 23/11)

Solving Inequalities

100

Solve the inequality:

x-7>5

x>12

200

Solve the inequality:
4x+3≤19

x≤4

300

Solve the inequality: 

-5x+8>23

x<-3

400

Solve the inequality: 

3(2x-1)≥5x+7

x≥10

500

Solve the compound inequality: 

-7<2x+1≤11

-4<x≤5

Graphing

100

A system of inequalities is:

y>x+1

y<5

Does the point (2,4) fall in the solution region?

Yes

200

For the inequality y≤-3, would you shade above or below the line?

Below the line

300

For the system: 

y>x+1

y<3

Where would you shade the lines?

Solution example: Line 1: Shade (above/below) Line 2: Shade (above/below)

Line 1: Above

Line 2: Below

400

A system of inequalities is:y

y≥3x-4

y<x+2

Does the point (2,1) fall in the solution region?

No

500

For the system:

y<2x+5

y>-x-2

Describe how you would graph it (direction + line type).

Ex: Line 1: Shade (above/below) (solid/dashed)

Line 2: Shade (above/below) (solid/dashed)

Line 1: Shade below (dashed)

Line 2: Shade above or on (solid)

Definitions

100

What is a system of equations?

A set of two or more equations with the same variables

200

What is an inequality?

A mathematical statement that compares two expressions using symbols like <, >

300

What is a solution to an inequality?

Any value that makes the inequality true

400

Which types of circles do you use for graphing inequalities on a graph?

Open and closed circles

500

What is a compound inequality?

An inequality that combines two inequalities using “and” or ”or”