Question 1. Solve the system of equations by substitution.
{ x + 5y = 5, 3x - 8y = -8
x = 0, y = 0; (0, 0)
x = 0, y = 1; (0, 1)
x = 1, y = 1; (1, 1)
x = 1, y = 0; (1, 0)
Question 2. Solve the problem.
The Paperback Trader is a book store that takes in used paperbacks for 20% of their cover price and sells them for 50% of their cover price. Pat brings in a stack of 16 paperback books to trade and gets $17.50 credit. Some of the books had a cover price of $7.97, the rest $3.97. She wants to get some Tom Clancy books having a cover price of $7.97. How many $7.97 books did she bring in and how many Clancy books can she get without paying any additional cash?
6 $7.97 books, 5 Clancy books
6 $7.97 books, 4 Clancy books
6 $7.97 books, 2 Clancy books
10 $7.97 books, 2 Clancy books
Question 3. Solve the system of equations by elimination.
{ 3x - 5y = -12, 6x + 8y = -24
x = 4, y = 0; (4, 0)
x = 0, y = -4; (0, -4)
x = 0, y = 4; (0, 4)
x = -4, y = 0; (-4, 0)
Question 4. Solve the system of equations. If the system has no solution, say that it is inconsistent.
{ x + y = -8, x + y = -4
x = -8, y = -4; (-8, -4)
x = 0, y = -12; (0, -12)
x = 0, y = 0; (0, 0)
inconsistent
Question 5. Solve the system of equations by elimination.
{ x +y = -3, x - y = 19
x = 3, y = 8; (3, 8)
x = 3, y = -11; (3, -11)
x = 8, y = 11; (8, 11)
x = 8, y = -11; (8, -11)
Question 6. Solve the system of equations by substitution.
{ 2x + 4y = 16, 5x = -15
x = -3, y = 3; (-3, 3)
x = -3, y = 0; (-3, 0)
x = 3, y = -3; (3, -3)
x = -3, y = -3; (-3, -3)
Question 7. Solve the system of equations by elimination.
{6x + 32y = 32, 6x - 8y = -8
x = 0, y = 1; (0, 1)
x = 1, y = 0; (1, 0)
x = 1, y = 1; (1, 1)
x = 0, y = 0; (0, 0)
Question 8. Solve the system of equations. If the system has no solution, say that it is inconsistent.
{ x - 4y = -10, 2x - 8y = -17
x = 4, y = 2; (4, 2)
x = 2, y = 4; (2, 4)
x = 2, y = 3; (2, 3)
inconsistent
Question 9. Solve the system of equations by substitution.
{ x + 7y = -2, 3x + y = 34
x = 7, y = 12; (7, 12)
x = -2, y = 3; (-2, 3)
x = 3, y = 7; (3, 7)
x = 12, y = -2; (12, -2)
Question 10. Solve the problem.
A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 7 slices of pizza and 4 soft drinks for $31.49. The second group bought 5 slices of pizza and 6 soft drinks for $26.61. How much does one slice of pizza cost?
$3.75 per slice of pizza
$1.31 per slice of pizza
$1.81 per slice of pizza
$3.25 per slice of pizza
Question 11. Solve the system of equations by elimination.
{ 2x + 12y = -50, 11x + 6y = 25
x = 11, y = -11; (11, -11)
x = 5, y = -5; (5, -5)
x = -5, y = 5; (-5, 5)
x = -6, y = 5; (-6, 5)
Question 12. Solve the system of equations. If the system has no solution, say that it is inconsistent.
{ 9x - 2y = -9, 9x - 2y = -8
x = 9, y = 2; (9, 2)
x = , y = ;
x = -9, y = -8; (-9, -8)
inconsistent
Question 13. Solve the problem.
A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many of them were adults?
24 adults
10 adults
16 adults
29 adults
Question 14. Solve the system of equations. If the system has no solution, say that it is inconsistent.
{ x/2 + y/3 = 4, x/4 + y/6 = 2
x = -1, y = ;
y = - x + 12, where x is any real number
or {(x, y) | y = - x + 12, where x is any real number}
x = 0, y = 12; (0, 12)
inconsistent
Question 15. Verify that the values of the variables listed are solutions of the system of equations.
{x + y = 7, x- y = -1
x = -3, y = 4
solution
not a solution
Question 16
Solve the system of equations by substitution.
{ x +y = -9, x - y = 13
x = 9, y = -11; (9, -11)
x = 9, y = 2; (9, 2)
x = 2, y = -11; (2, -11)
x = 2, y = 11; (2, 11)
Question 17. Solve the system of equations by elimination.
{ 5x - 2y = -1, x + 4y = 35
x = 2, y = 9; (2, 9)
x = 3, y = 9; (3, 9)
x = 2, y = 8; (2, 8)
x = 3, y = 8; (3, 8)
Question 18. Solve the problem.
An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?
153 mi
132 mi
147 mi
168 mi
Question 19. Solve the system of equations by elimination.
{ 6x + 3y = 51, 2x - 6y = 38
x = -10, y = 3; (-10, 3)
x = -3, y = 10; (-3, 10)
x = 10, y = -3; (10, -3)
x = 3, y = -10; (3, -10)
Question 20. Verify that the values of the variables listed are solutions of the system of equations.
{ x + y = -5, x - y = 1
x = -2, y = -3
solution
not a solution
Question 21. Solve the system of equations by elimination.
{ 5x + 6y = 60, 5x + 2y = 80
x = -5, y = 18; (-5, 18)
x = -18, y = 5; ( -18, 5)
x = 18, y = -5; (18, -5)
x = -18, y = 6; (-18, 6)
Question 22. Solve the system of equations by substitution.
{ 5x - 2y = -1, x + 4y = 35
x = 3, y = 8; (3, 8)
x = 2, y = 8; (2, 8)
x = 3, y = 9; (3, 9)
x = 2, y = 9; (2, 9)
Question 23. Solve the system of equations. If the system has no solution, say that it is inconsistent.
{ x + 2y = - 8, -4x - 8y = 32
x = -8, y = 0; (-8, 0)
x = 0, y = 0; (0, 0)
y = - - 4, where x is any real number
or {(x, y) | y = - - 4, where x is any real number}
inconsistent
Question 24. Solve the system of equations by substitution.
{ 5x + 3y = 80, 2x + y = 30
x = 10, y = 10; (10, 10)
x = 0, y = 0; (0, 10)
x = 10, y = 0; (10, 0)
x = 0, y = 10; (0, 10)
Question 25. Solve the system of equations. If the system has no solution, say that it is inconsistent.
{ 4x + y = 5, -16x - 4y = -20
x = -4y + 5, where y is any real number
or {(x, y) |x = -4y + 5, where y is any real number}
y = -4x + 5, where x is any real number
or {(x, y) | y = -4x + 5, where x is any real number}
y = 4x + 5, where x is any real number
or {(x, y) | y = 4x + 5, where x is any real number}
inconsistent