Solving Systems of Linear equations
Additional Exercises 5.2
Form I
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. _______________
Additional Exercises 5.2
Form II
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. _______________
Additional Exercises 5.2
Form III
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. _______________