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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
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Solving Systems of Linear equations

Solve each system by the substitution method. If there is no solution or infinitely many solutions,
so state. Use set notation to express solution sets.

1.
y = x + 3
x + 2y = 18

1. _______________

2.
2x − 2y = 2
x = 3y + 5

2. _______________

3.
3x − 2y = 9
y = 2x − 5

3. _______________

4.
2x − y = 15
y = x − 5

4. _______________

5.
3x + 3y =12
x = 4 − y

5. _______________

6.
3x + y = 10
5x − 2y = 2

6. _______________

7.
x − 5y = 35
4x + 2y = 8

7. _______________

8.
12x − 4y = 16
3x − y = −4

8. _______________

9.
5x + y = −10
2x − 6y = −4

9. _______________

10.
x + 8y = −56
− 2x + 9y = −63

10. ______________

11.
6x + 4y = 12
2x − 2y = −14

11. ______________

12.
3x − 2y = 25
4x + 8y = −20

12. _______________

13.
2x + 3y = 9
3x + 2y = 1

13. _______________

14.
2x + y = 14
4x + 2y = −28

14. _______________

15.
x = 8 − 5y
x = 3y − 8

15. _______________

16.
y = 2x + 3
y = 4x + 7

16. _______________

Solve each system by the substitution method. If there is no solution or infinitely many solutions,
so state. Use set notation to express solution sets.

1.
x = 1− 6y
2x + 8y = 6

1. _______________

2.
y = 3x + 4
5x − y = 4

2. _______________

3.
6x − 2y = 14
3x − y = 7

3. _______________

4.
x + 5y = 18
2x + 2y = 20

4. _______________

5.
6x + y = −12
5x + 2y = 4

5. _______________

6.
9x − 3y = 3
3x − y = 12

6. _______________

7.
x + 7 y = 1
2x + 8y = 2

7. _______________

8.
2x + y = 14
6x − 3y = 18

8. _______________

9.
2x + y = 8
− 3x + 2y = −19

9. _______________

10.
6x − y = −1
6x − 5y = −17

10. ______________

11.
5x −10y = 6
x − y = 1

11. ______________

12.
7x +15y = 12
x + 9y = 4

12. _______________

13.
x − 3/4y =3
-2x + 3/2y = -5

13. _______________

14.
1/4x + 1/2y = 5
4x - y = 26

14. _______________

15.
3x − 2y = 3
-4/3x + y = 1/3

15. _______________

16.
3x + 6y = 3
2x + 8y = 22

16. _______________

Solving Systems of Linear equations by the Substitution Method
Solve each system by the substitution method. If there is no solution or infinitely many solutions,
so state. Use set notation to express solution sets.

1.
4x + 3y = 11
y = 2x −13

1. _______________

2.
5x − 3y = 11
x = 12 + 2y

2. _______________

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

3. _______________

4.
x = 5y − 35
5x − 6y = −61

4. _______________

5.
2x + y = 14
4x + 2y = 28

5. _______________

6.
5x + 5y = 0
x − y = −4

6. _______________

7.
x + 2y = 32
3x − 5y = −14

7. _______________

8.
4x −12y = 15
x − 3y = 4

8. _______________

9.
6x + 4y = 12
2x − 4y = −44

9. _______________

10.
x + 3y = −1
8x − 8y = 4

10. ______________

11.
15x − y = 14
3x − 4y = 18

11. ______________

12.
4/5x + 1/2y = 6
3x + y = 19

12. _______________

13.
1/3x + 1/3y = 0
x − y = 14

13. _______________

14.
1/2x - 2/3y = -1
3/7x + y = 18

14. _______________

15. An electronic company kept comparative statistics on two
products, A and B. For the years 1980 to 1988, the total number
of Product A sold (in thousands) is given by the equation
y = 72x + 689where x is the number of years since 1980. For
the same time period, the total number of Product B sold (in
thousands) is given by the equation y = −30x + 434, where x is
the number is years since 1980. Use the substitution method to
solve the system and describe what the solution means.

15. _______________

16. One number is 1 less than a second number. Twice the second
number is 19 less than 5 times the first. Find the two numbers.

16. _______________