Systems of Linear Equations and Inequalities

Solving Systems by Graphing

100

Solve the following by graphing
y=-x+5
y=-2x+3

(-2,7)

200

Solve the following by graphing
y=3x-5
-7x+y=-5

(0,-5)

300

Solve the following system by graphing 

2y+4x=12

 2x-y=-10

(-1,8)

400

Solve the following system by graphing.

 4x+2y=6 

3x-3y=9

(2,-1)

500

Solve the following system by graphing 

y=4x+4 

2y=-3x-14

(-2,-4)

Solving Systems by Substitution

100

Solve the following system using Substitution 

x=6-4y

 2x-3y=1

(2,1)

200

Solve the following system using substitution 4x+3y=0

 y=-2x-2

(-3,4)

300

Solve the following system using substitution 

6x-y=-35 

5x-2y=-35

(-5,5)

400

Solve the following system using substitution 3x+3y=-18 

4x-y=-14

(-4,-2)

500

Solve the following system using substitution 

4x-2y=-4 

7x-5y=-19

(3,8)

Solving Systems by Elimination

100

Solve the following system using elimination x+5y=28 

x+2y=13

(3,5)

200

Solve the following system using elimination. 

7x-4y=-30 

3x+4y=10

(-2,4)

300

Solve the following system using elimination 

x-3y=6

 2x=-3y-33

(-9,-5)

400

Solve the following system using Elimination. x+3y=-1 

5x-4y=-24

What is (-4,1)?

500

Solve the following system using elimination. 

3x-5y=-16 

2x-3y=-8

What is (8, 8)?

Determining the number of Solutions

100

Determine whether the system is consistent or inconsistent. If it is consistent, tell whether it is dependent or independent. 

-6x+2y=-2

 3x-y=2

Inconsistent. No solution; the lines are parallel.

200

Determine whether the system is consistent or inconsistent. If it is consistent, tell whether it is dependent or independent.

 2y-x=-4 

2x+y=3

Consistent; Independent (2,-1) One solution

300

Determine whether the system is consistent or inconsistent. If it is consistent, tell whether it is dependent or independent.

 x+2y=3 

x-2y=2

Consistent; Independent. One solution (5/2, 1/4)

400

Determine whether the system is consistent or inconsistent. If it is consistent, tell whether it is dependent or independent. 

2x-y=4 

-2x+y=-4

Consistent; Dependent. They are the same line.

500

Determine whether the system is consistent or inconsistent. If it is consistent, tell whether it is dependent or independent.

 y+3=4x

 3y=12x-9

Consistent; Dependent. They are the same line.

Systems of Linear Inequalities

100

Solve the systems of linear inequalities. 

y>-x+3

y<-2x+4

Check with desmos.com

200

Solve the system of Linear inequalities.

 y>=-x+2 

2y<-2x +8

Check with desmos.com

300

Solve the linear system of inequalities. 

y>=3  

 y>2x+1

Check with desmos.com

400

Solve the system of linear inequalities. 

x+y>1  

 x<=y

Check with desmos.com

500

Solve the following system of linear inequalities. (1/2)x+y>=3   

 x>-1

Check with desmos.com