1-3 Determine whether or not the following ordered pairs are solutions to the given systems of equations. Answer Solution or Not a Solution.

1) (4,1)2) (-2,1) 3) (7,-6)

4-6. Solve the following linear systems by graphing.

4) 5) 6)

7-8. Solve the following linear systems using substitution.

7) 8)

9-10. Solve the following linear systems using elimination.

9) 10)

11-13. Solve the following linear systems algebraically (using substitution or elimination).

11) 12) 13)

14-15. Determine whether the following systems have one solution, no solution, or infinite solutions.

14) 15)

16-21. Graph the system of linear inequalities.

16) 17) 18)

19) 20)21)

Solve the linear system by using elimination.

  1. 6x – y = 5
3x + y = 4 /
  1. x + 4y = 9
–x – 2y = 3
  1. 5x – 3y = –14
x + 3y = 2 /
  1. 2x + y = 7
x + y = 1
  1. 4x + 3y = 18
4x – 2y = 8 /
  1. 3x = y + 5
2x + y = 5
  1. x – 4y = –19
3y –15 = x /
  1. y – 3 = –2x
2x + 3y = 13

Solve the linear system by using elimination.

  1. 6x – 3y = 36
5x = 3y + 30 /
  1. –4x + y = –27
–y + 6x = 43
  1. 9x – 4y = –55
3x = –4y – 21 / 33. –5x + 2y = 22
3x + 2y = –10

Solve the linear system by using elimination.

REARRANGE FIRST

  1. x + 5y = –8
–x –2y = –13
  1. 7x – 4y = –30
3x + 4y = 10
  1. 6x + y = 39
–2x + y = –17
  1. 3x = y –20
–7x 2y = 40
  1. 2x –6y = –10
4x = 10 + 6y
  1. x –3y = 6
–2x = 3y + 33
  1. –3x = y –20
–y = –5x + 4
  1. 4x – y = –21
– 4x+7y = 51
  1. –2x + 5y = 14
8x + 5y = 94
  1. –y – x = 7
x = 6y – 28
  1. 10y – 2x = –38
– 2x = 8y + 52
  1. –15x + 4y = 43
4y = – 3x + 25

Solve the linear system by using elimination.

  1. 6x – y = 5

3x + y = 4

  1. x + 4y = 9

–x – 2y = 3

  1. 5x – 3y = –14

x + 3y = 2

  1. 2x + y = 7

x + y = 1

  1. 4x + 3y = 18

4x – 2y = 8

51. –5x + 2y = 22

3x + 2y = –10

  1. 3x = y + 5

2x + y = 5

  1. x – 4y = –19

3y –15 = x

  1. y – 3 = –2x

2x + 3y = 13

  1. 6x – 3y = 36

5x = 3y + 30

  1. –4x + y = –27

–y + 6x = 43

  1. 9x – 4y = –55

3x = –4y – 21

Solve the linear system by using elimination.

  1. x + y = 3
–2x + 4y = 6 /
  1. 4x + y = –8
3x + 3y = 3
  1. 3x – y = 10
2x + 5y = 35 /
  1. 5x – 4y = 42
x – 6y = 24
62. 2x + 3y = –10
–4x + 5y = –2 /
  1. 5x + 6y = 100
2x + 3y = 46
  1. 3x – 5y = –50
12x + 2y = –46 /
  1. –6x – 5y = –43
7x + 15y = 41
  1. 8x – 6y = 8
4x + 5y = 36 /
  1. 4x + 5y = 100
3x – 2y = 6
  1. –3x + 11y = –38
2x + 9y = –40 /
  1. 5x – 8y = –35
–7x – 3y = –22
  1. Baseball Game Two families go to a baseball game. One family purchases two adult tickets and three youth tickets for $33. Another family purchases three adult tickets and two youth tickets for $37. Let x represent the cost in dollars of one adult ticket and let y represent the cost in dollars of one youth ticket. The linear system given by 2x + 3y = 33 and 3x + 2y = 37 represents this situation.
  2. Solve the linear system to find the cost of one adult and one youth ticket.
  3. How much would it cost two adults and five youths to attend the game?
  1. Electricians Two different electrical businesses charge different rates.

Business A charges $30 for a service call, plus an additional $45 per hour for labor. Business B charges $45 for a service call, plus an additional $40 per hour for labor.

a.Let x represent the number of hours of labor and let y represent the total charge in dollars. Write a linear system that you could use to find the lengths of a service call for which both businesses charge the same amount.

b.Solve the linear system.

c.When will the businesses charge the same amount?

  1. Is (5,2) a solution to Shade the areas 1st then check your point

  1. Graph

Solve by graphing. Then use your answers to fill in the puzzle below.

74) 2y – x = -42x + y = 375)x – y = 8x + y = -2

76)5x – y = -9y + 2x = 277)6x + 2y = 8-3x + 4y = 16

78)-9x + 6y = -62x – 3y = 879)y = 3xy = 4x - 1

80) -3x – y = - 12x + 4y = -1681) 2x + y = -4x – y = -8

82) x – y = 93x + 2y = 283)4x + 3y = 02x + y = -2

Version A:

What did the dairy man say to the thieves?

______

5 3 7 106 4 1 2 892

Find the answer to each of the ten problems, and plug that answer in above the give problem number.

( - 2, - 4) N(-3,4) H(0,4) C( -1, 4) A(2,-5) C

(1,3) O(2, -1) H(3, -5) E(4, -5) S(-4, 4) E

Version B:

What did the dairy man say to the thieves?

______

1 2 3 4 5 9 1 6 7 10 8 4

Find the answer to each of the ten problems, and plug that answer in above the give problem number.

( - 2, - 4) V(-3,4) O(0,4) E( -1, 4) T(2,-5) L

(1,3) C(2, -1) N(3, -5) O(4, -5) E(-4, 4) S

84.Given that the slope of a perpendicular line (P) is the negative reciprocal of its slope (m), which equation is equivalent to ?

a. /
b. /
c. /
d. /

85.The high school cross country coach has a budget of $210 to buy new stopwatches and GPS measuring devices. He buys a GPS measuring devise that costs $62 and spends the rest of his budget on stopwatches that cost $9.25 each. What is the greatest number of stopwatches that he can buy and stay within his budget?

a. / 6
b. / 16
c. / 19
d. / 148

86.The high school cross country coach has a budget of $230 to buy new stopwatches and GPS measuring devices. He buys a GPS measuring devise that costs $77 and spends the rest of his budget on stopwatches that cost $8.25 each. What is the greatest number of stopwatches that he can buy and stay within his budget?

a. / 153
b. / 21
c. / 18
d. / 7

87.The high school cross country coach has a budget of $220 to buy new stopwatches and GPS measuring devices. He buys a GPS measuring devise that costs $73 and spends the rest of his budget on stopwatches that cost $6.75 each. What is the greatest number of stopwatches that he can buy and stay within his budget?

a. / 147
b. / 24
c. / 21
d. / 8

88.A aquarium has a total of 27 beta fish, piranhas, and turtles. The number of piranhas is 2 more than the number of turtles, and 2 fewer than the number of beta fish. How many beta fish are there in the aquarium?

a. / 9
b. / 11
c. / 13
d. / 8

89.A aquarium has a total of 19 beta fish, piranhas, and turtles. The number of piranhas is 2 more than the number of turtles, and 3 fewer than the number of beta fish. How many beta fish are there in the aquarium?

a. / 9
b. / 11
c. / 7
d. / 6

90.A pet store has a total of 17 snakes, guinea pigs, and miniature poodles. The number of guinea pigs is 1 more than the number of miniature poodles, and 3 fewer than the number of snakes. How many snakes are there in the pet store?

a. / 5
b. / 8
c. / 10
d. / 6

91.A day at the local water park costs $10 for admission plus an additional $2.75 for each food item. John has $29 to spend at the water park. What is the maximum number of food items John can purchase?

a. / 5
b. / 7
c. / 12
d. / 6

92.A day at the local water park costs $15 for admission plus an additional $2.75 for each food item. John has $32 to spend at the water park. What is the maximum number of food items John can purchase?

a. / 12
b. / 7
c. / 5
d. / 6

93.A day at the local water park costs $10 for admission plus an additional $2.75 for each food item. Andy has $26 to spend at the water park. What is the maximum number of food items Andy can purchase?

a. / 4
b. / 10
c. / 5
d. / 6

94.Which graph represents the solution to the system of equations below?

a. / / c. /
b. / / d. /

95.Which graph represents the solution to the system of equations below?

a. / / c. /
b. / / d. /

96.Which graph represents the solution to the system of equations below?

a. / / c. /
b. / / d. /

97.Which system of inequalities is graphed below?

a. /
b. /
c. /
d. /

98.Which system of inequalities is graphed below?

a. /
b. /
c. /
d. /

99.Which system of inequalities is graphed below?

a. /
b. /
c. /
d. /

100.What is the slope of a line parallel to the graph of

a. /
b. /
c. /
d. / 2

101.What is the slope of a line parallel to the graph of

a. /
b. /
c. / 6
d. /

102.What is the slope of a line parallel to the graph of

a. /
b. /
c. / 7
d. /

103.What is the value of x in the solution for the system of equations shown below?

a. / 7
b. / 6
c. /
d. / -6

104.What is the value of x in the solution for the system of equations shown below?

a. / 10
b. / 7
c. / -10
d. /

105.What is the value of x in the solution for the system of equations shown below?

a. / -6
b. / 6
c. / 3
d. /

106.Which point on the grid below is the solution to the following system of equations?

a. / A
b. / B
c. / C
d. / D

107.What is the solution to the following system of equations?

a. / (13, –7)
b. / (–7, –6)
c. / (6, 7)
d. / (–7, 6)

108.What is the solution to the following system of equations?

a. / (7, –5)
b. / (8, 5)
c. / (–5, –8)
d. / (–5, 8)

109.What is the solution to the following system of equations?

a. / (–14, 9)
b. / (3, –9)
c. / (9, 3)
d. / (9, –3)

110.What is the solution to this system of equations?

a. / (–2, 7)
b. / (2, –7)
c. / infinite solutions
d. / no solutions

111.What is the solution to this system of equations?

a. / no solutions
b. / (–4, –2)
c. / (4, 2)
d. / infinite solutions

112.What is the solution to this system of equations?

a. / no solutions
b. / (–4, –2)
c. / (4, 2)
d. / infinite solutions

113.Two painters were working together to finish painting a house. One can paint 45 square feet in 2 hours, and the other can paint 45 square feet in 6 hours. How much paint can they finish together in 12 hours working together?

a. / 360 square feet
b. / 4 square feet
c. / 370 square feet
d. / 360 square feet

114.Two painters were working together to finish painting a house. One can paint 35 square feet in 4 hours, and the other can paint 35 square feet in 7 hours. How much paint can they finish together in 8 hours working together?

a. / 120 square feet
b. / 385 square feet
c. / 110 square feet
d. / 8 square feet

115.Two painters were working together to finish painting a house. One can paint 35 square feet in 2 hours, and the other can paint 35 square feet in 7 hours. How much paint can they finish together in 12 hours working together?

a. / 280 square feet
b. / 315 square feet
c. / 4 square feet
d. / 270 square feet

116.Toni mixed some 15% fruit juice with some 80% fruit juice to obtain 25 gallons of a 35% fruit juice. Let f represent the amount of 15% fruit juice that Toni added. Which equation can be used to solve for f ?

a. /
b. /
c. /
d. /

117.Amy mixed some 50% fruit juice with some 75% fruit juice to obtain 15 gallons of a 55% fruit juice. Let f represent the amount of 50% fruit juice that Amy added. Which equation can be used to solve for f ?

a. /
b. /
c. /
d. /

118.Marcy mixed some 35% fruit juice with some 65% fruit juice to obtain 20 gallons of a 40% fruit juice. Let f represent the amount of 35% fruit juice that Marcy added. Which equation can be used to solve for f ?

a. /
b. /
c. /
d. /