Algebra II Name:

Worksheet #1 (§3 – 5) Solving Systems of Equations: Graphing Solve each system of equations by GRAPHING. Graph each line. The point where the two lines intersect is called the “solution” of the system. Give the coordinates for that point. This assignment will be easier if you use a ruler.

1.

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2 x + y = 33y = x " 12

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2.

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3x " 4y = "12y = "2 x " 8

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3.

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y = "x + 4

y = "3

5x + 2

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& %

4.

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3x + y = "22y = 3x + 14

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Algebra II Name:

Worksheet #2 (§3 – 5) Solving Systems of Equations: Substitution Solve each system of equations using SUBSTITUTION.

EX

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2 x + 3 y = 31y = x + 7

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2 x + 3 x + 7( ) = 31

2 x + 3 x + 21 = 315 x = 10

x = 2

!

y = 2 + 7y = 9

Answer:

!

2 , 9( )

1.

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y = xy = "x + 2

2.

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y = x + 4y = 3x

3.

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y = 3x " 10y = 2 x " 5

4.

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x = "2y + 1x = y " 5

5.

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y = 5x + 5y = 15x " 1

6.

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y = x " 3y = "3x + 25

7.

!

y = x " 72 x + y = 8

8.

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y = 3x2 x + y = 10

9.

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x + 2y = 200x = y + 50

Algebra II Name:

Solve each system of equations using SUBSTITUTION.

10.

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x = y " 35x + 3y = 1

11.

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3x " y = 7y = 2 x " 4

12.

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y = x " 42 x " 3y = 11

13.

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x = 2y + 73y " x = 8

14.

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y = 10 " 2 x3x " 2y = 22

15.

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y = 50x + 4y " 32 x = 40

16.

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y = 2 x " 2y = x + 2

17.

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y = x " 43x " 2y = 11

18.

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x = 3y " 42 x + 6y = 5

19.

!

x = 3y + 9y = "2 x + 25

20.

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x = 2y + 7x = y + 4

Answers:

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1. 1 , 1( ) 3. 5 , 5( ) 5. 35

, 8" # $ %

& ' 7. 5 , (2( )

9. 100 , 50( ) 11. 3 , 2( ) 13. 37 , 15( )15. 2 , 104( ) 17 , 3 , (1( ) 19. 12 , 1( )

Algebra II Name:

Worksheet #3 (§3 – 5) Solving Systems of Equations: Elimination

Solving systems of equations using ELIMINATION.

EX:

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2 x " y = 42 x + 3y = "12

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(1) MULTIPLY the first equation by

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"1. ADD the new equation and the second equation. This “eliminates” the “x”s.

!

2 x " y = 4 # "1( )

$ % $ $ $ $ "2 x + y = "4

2 x + 3y = "12 $ % $ $ $ $ 2 x + 3y = "12

!

4y = "164y

4=

"16

4y = "4

(2) SUBSTITUTE to find x…

!

2 x " "4( ) = 4

2 x + 4 = 42 x = 0

x = 0

The solution is

!

0 , 4( )

Solve each system of equations using the ELIMINATION method.

1.

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x + 2y = 73x " 2y = "3

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2.

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2 x + 5y = "1x + 2y = 0

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3.

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9x " 3y = 247x " 3y = 20

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4.

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4x " y = 63x + 2y = 21

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Algebra II Name:

Solve each system of equations using the ELIMINATION method.

5.

!

2 x " 3y = "113x + 2y = 29

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6.

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"2 x + 3y = "9x + 3y = 3

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7.

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"2 x + 3y = 25"2 x + 6y = 58

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8.

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"x + 8y = "323x " y = 27

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9.

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6x + 3y = 0"3x + 3y = 9

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10.

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6x + 3y = 27"4x + 7y = 27

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11.

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5x + 7y = "14x " 2y = 22

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12.

!

4x " 3y = 113x " 5y = "11

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Answers:

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1. 1 , 3( ) 3. 2 , "2( ) 5. 5 , 7( ) 7. 4 , 11( ) 9. "1 , 2( ) 11. 4 , "3( )

Algebra II Name:

Worksheet #4 (§3 – 5) Parallel Lines / Common Line

A system of equations has NO SOLUTION if the lines are PARALLEL because there is no point of intersection.

• When using either substitution or elimination to solve the system, if all of the variables cancel and the result is FALSE, then the SYSTEM has NO SOLUTION. The lines are PARALLEL.

A system of equations has infinitely MANY SOLUTIONS when the two equations represent the same line. The solution is all points on the line.

• When using either substitution or elimination to solve the system, if all of the variables cancel and the result is TRUE, then the SOLUTION is the set of ALL POINTS ON THE COMMON LINE.

Use substitution to solve each system of equations. State whether the system has no solution or all points on the common line.

1.

!

y =3

4x + 2

3

4x " y = 4

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$ % %

& % %

2.

!

y = "3x " 43x + y = "4

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3.

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y = "x + 23x + 3y = 12

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4.

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x = y + 4y = x + 4

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5.

!

3x " 6y = 12x " 2y = 4

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6.

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4x + y = 6y = "4x + 1

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Algebra II Name:

Use substitution to solve each system of equations. State whether the system has no solution or all points on the common line.

7.

!

y =2

3x + 4

2 x " 3y = 3

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$ %

& %

8.

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2 x + y = 63y = "6x + 9

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9.

!

y = 3x " 6"3x + y = "6

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10.

!

3x + y = 10y = "3x + 4

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11.

!

4x + 2y = 8y = "2 x + 4

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12.

!

6x " 3y = 6y = 2 x + 5

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13.

!

y = "2

3x + 4

2 x + 3y = "6

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$ %

& %

14.

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2 x + 3y = 83

2y = 4 " x

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& %

15.

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5x + 2y = 6

y = "5

2x + 1

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& %

16.

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y = "2

3x + 1

4x + 6y = 6

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$ %

& %

17.

!

y =1

3x + 10

x = 3y + 6

"

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% $

18.

!

3x " 2y = 10

y =3

2x " 1

#

$ %

& %

Answers: 1.no solution, 3.no solution, 5.all points on x – 2y = 4, 7.no solution, 9.all points on y = 3x – 6, 11.all point on y = –2x + 4, 13.no solution, 15.no solution, 17.no solution

Algebra II Name:

Worksheet #5 (§3 – 5) Solving Systems of Equations by Elimination Solve each system of equations using the ELIMINATION method. Each system has exactly one point as a solution.

Solutions:

!

1. 1 , 3( ) 3. 7 , 6( ) 5. 2 , 0( ) 7. 2 , "2( ) 9. 18 , 12( ) 11. "1 , 5( ) 13. 5 , 7( ) 15. 0 , 0( )17. 8 , 7( ) 19. 4 , 11( ) 21. 11 , 7( ) 23. 7 , "3( ) 25. "1 , 2( ) 27. 8 , "1( ) 29. 4 , "3( )

Algebra II Name:

Worksheet #6 (§3 – 5) Solving Systems of Equations: Elimination Solve each system of equations using the ELIMINATION method.

1.

!

x " y = 5x + y = 7

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2.

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x + y = 12 x " y = 5

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3.

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3x + y = 4x + y = 2

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4.

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x " 3y = 4x + 5y = "4

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5.

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3x + y = 7x + 2y = 4

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6.

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x " 2y = 73x " 2y = 9

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7.

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3x " y = 46x " 2y = 8

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8.

!

x " 2y = "3"2 x + 4y = 6

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9.

!

2 x + 5y = 94x " 7y = "16

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10.

!

5x " 3y = 142 x + 3y = "7

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Algebra II Name:

Solve each system of equations using the ELIMINATION method.

11.

!

8x " 3y = 214x + 5y = "9

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12.

!

4x " 6y = 52 x " 3y = 7

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13.

!

3x + 6y = 72 x + 4y = 5

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14.

!

3x " 5y = 7x " 2y = 3

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15.

!

3x + 4y = 252 x + y = 10

" # $

16.

!

3x + 2y = 162 x " 3y = "11

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17.

!

2 x " 5y = 135x + 3y = 17

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18.

!

4x + 4y = 52 x " 8y = "5

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19.

!

3x + 7y = 164x " 3y = 9

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20.

!

3x " 6y = 69x " 3y = 8

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Answers:

!

1. 6 , 1( ) 3. 1 , 1( ) 5. 2 , 1( ) 7.all points on the line 3x " y = 4 9. " 12

, 2# $ % &

' ( 11. 3

2, "3#

$ % &

' ( 13.no solution

15. 3 , 4( ) 17. 4 , "1( ) 19. 3 , 1( )

Algebra II Name:

Worksheet #7 (§3 – 5) Solving Systems of Equations Solve each system of equations using SUBSTITUTION or ELIMINATION. These systems may have…

• a single point solution, • no solution (parallel lines) or • may represent the same line (the line is the solution).

Solutions:

!

1. 1 , 2( ) 3.no solution 5. 7 , 4( ) 7. "5 , 2( ) 9. "1 , "1( ) 11. 6 , 6( ) 13.no solution 15. 7 , 11( )17. 8 , 7( ) 19. 5 , 6( ) 21. 5 , 4( ) 23.no solution 25. 1

2, 1

2

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' ( 27. " 1

2, 0#

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