Unit Quiz
Overview
Test your mastery of linear equations and systems. This comprehensive quiz covers all concepts from the unit including graphing, substitution, word problems, and error identification.
Quiz Questions
Question 1: Solve the system by substitution: y = x + 5 and 2x + y = 14
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Answer: (3, 8)
Substitute y = x + 5: 2x + (x + 5) = 14, 3x = 9, x = 3. Then y = 3 + 5 = 8.
Question 2: What is the solution to the system y = -x + 6 and y = 2x?
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Answer: (2, 4)
Set equal: 2x = -x + 6, 3x = 6, x = 2. Then y = 2(2) = 4.
Question 3: How many solutions does the system y = 4x - 3 and 8x - 2y = 6 have?
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Answer: Infinitely many solutions
Rewrite second equation: -2y = -8x + 6, y = 4x - 3. Same as the first equation!
Question 4: Solve: 3x + y = 11 and x - y = 1
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Answer: (3, 2)
Add equations: 4x = 12, x = 3. Then 3 - y = 1, y = 2.
Question 5: A rectangle's length is 3 times its width. The perimeter is 48 cm. Find the dimensions.
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Answer: Width = 6 cm, Length = 18 cm
L = 3W and 2L + 2W = 48Jean. Substitute: 2(3W) + 2W = 48, 8W = 48, W = 6, L = 18.
Question 6: The system y = 5x + 2 and y = 5x - 7 has how many solutions?
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Answer: No solution (zero solutions)
Both lines have slope 5 but different y-intercepts, so they're parallel and never intersect.
Question 7: Solve: 2x - 3y = -1 and x + 2y = 12
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Answer: (4.57, 3.71) or approximately (32/7, 26/7)
From second: x = 12 - 2y. Substitute: 2(12-2y) - 3y = -1, 24 - 7y = -1, y = 25/7. Then x = 12 - 50/7 = 34/7.
Question 8: Adult tickets cost $15 and student tickets cost $10. If 200 tickets were sold for $2,500, how many adult tickets were sold?
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Answer: 100 adult tickets
a + s = 200 and 15a + 10s = 2500. Substitute s = 200 - a: 15a + 10(200-a) = 2500, 5a = 500, a = 100.
Question 9: If the point (2, 5) is a solution to the system ax + y = 9 and x + by = 12, find a and b.
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Answer: a = 2, b = 2
Substitute (2, 5): 2a + 5 = 9, so a = 2. And 2 + 5b = 12, so b = 2.
Question 10: Solve: y = 3x - 2 and 6x - 2y = 4
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Answer: Infinitely many solutions
Substitute y = 3x - 2: 6x - 2(3x - 2) = 4, 6x - 6x + 4 = 4, 4 = 4. This is always true, so infinite solutions.