1. Solve by graphing. y = 3x − 7 y − 2x = − 6
Question 1
(1, -4)
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2. Solve by graphing. y − 3x = − 2 y = 3x + 5
Question 2 No
solution
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3. Solve by graphing. x − 4y = − 17 y = 4x + 8
Question 3
(-1, 4)
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4. Solve by graphing. x + y = − 2 x − y = 2
Question 4
(0, -2)
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5. Solve by substitution. 3y = x + 6 x = 2y − 2
Question 5
(6, 4)
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6. Solve by substitution. 2x + 3y = − 4 x + y = 1
Question 6
(7, -6)
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7. Solve by substitution. y = x + 6 y = 2x + 9
Question 7
(-3,3)
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8. Solve by substitution. 2y = − 5x + 5 5x – 5 = −2y
Question 8
Infinitely
many
solutions
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9. Solve by Elimination. 3x − 5y = 9 3x - 4y = − 6
Question 9
(-22, -15)
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10. Solve by Elimination. 2x − 6y = − 33 x + 2y = 8.5
Question 10
(-1.5, 5)
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11. Solve by elimination. 4x − 10y = −24 3x + 5y = −18
Question 11
(-6, 0)
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12. Solve by elimination. x − 2y = 23 2x + y = 1
Question 12
(5, -9)
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13. John paid $34 for two algebra and three geometry books
John paid $34 for two algebra and three geometry books. He paid $36 for three algebra and two geometry books. What is the cost of each book?
Question 13
Algebra = $8
Geometry = $6
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14. The sum of two numbers is 14
The sum of two numbers is 14. If one of the numbers is doubled, the sum will become 22. What are the numbers?
Question 14
8 and 6
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15. Peter invested $450 in insurance and stocks
Peter invested $450 in insurance and stocks. He put $50 more in insurance than stocks. How much did he invest in each?
Question 15
$200 in stocks
$250 in insurance
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16. The measure of one of two supplementary angles is three times the measure of the other angle. What are the measures of the angles?
Question 16 3x x
45˚ and
135˚
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17. The slope is the same and the y-intercept is different.
If a system of linear equations has no solution, what does that tell you about the slopes and y-intercepts of the graphs of the equations?
Question 17
The slope is the same and the y-intercept is different.
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18. Write a system of linear equations that has no solution and a system of equations that has infinitely many solutions.
Question 18
No solution: both of the equation must have the same slope.
Infinitely many solutions: both equations are the same.
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19. What does it mean to break even?
Question 19
The cost and the profit are the same.
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20. The parent-teacher organization is selling baskets of cookies for a school fundraiser. The materials needed to make each basket cost $3.75, and the baskets are being sold for $10 each. If they spend $75 to advertise their sale, how many baskets must be sold in order to break even?
Question 20
12 baskets
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21. If a system of linear equation has infinitely many solutions, what do you know about the slopes and y-intercepts of the graphs?
Question 21
The slope and the y-intercept are the same.
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22. Write a system of equations that you could solve by using substitution
Write a system of equations that you could solve by using substitution. For example: y = 6x y + 3 = 2x
Question 22