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Quizzes > High School Quizzes > Mathematics

Solving Systems of Elimination Practice Quiz

Conquer worksheet challenges and elimination strategies

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art promoting Eliminate Conquer, a strategic high school algebra challenge trivia.

Easy
Solve the system: x + y = 10, and x - y = 2. What is the value of x?
6
8
4
7
Adding the two equations eliminates y, yielding 2x = 12 which simplifies to x = 6. Once x is determined, the system becomes straightforward.
Solve the system: 2x + 3y = 20 and 2x - y = 4. What is the value of y?
5
2
3
4
Subtracting the second equation from the first cancels the x terms, resulting in 4y = 16. Dividing by 4 gives y = 4.
Find the value of x in the system: x + 2y = 10 and x - y = 1.
6
5
4
3
By rearranging the equation x - y = 1 to get x = y + 1 and substituting into x + 2y = 10, you obtain 3y = 9 which gives y = 3 and hence x = 4.
Solve the system: x + 2y = 12 and x - 2y = 4. What is the value of x?
7
9
8
6
Adding the two equations cancels the y terms, resulting in 2x = 16. Dividing by 2 gives x = 8.
Solve the system: 4x + 2y = 20 and 4x - 2y = 4. What is the value of y?
2
4
5
3
By adding the two equations, the y terms cancel to give 8x = 24, so x = 3. Substituting back into one of the equations results in y = 4.
Medium
Solve the system: 3x + 4y = 18 and 2x - 4y = 2. What is the value of x?
6
5
4
3
Adding the two equations eliminates y and yields 5x = 20. Dividing by 5, we find x = 4.
Solve the system: 3x - y = 8 and 2x + y = 7. What is the value of x?
5
4
2
3
Adding the two equations cancels y, which results in 5x = 15 and thus x = 3.
Solve the system: 4x + 3y = 25 and 4x - 3y = 7. What is the value of x?
6
5
4
3
By adding the equations, the y terms cancel, leaving 8x = 32. Dividing by 8 yields x = 4.
Solve the system: 2x - y = 1 and 3x + y = 14. What is the ordered pair solution (x, y)?
(3, 6)
(4, 4)
(2, 3)
(3, 5)
Adding the equations eliminates y, giving 5x = 15, so x = 3. Substituting back into one equation results in y = 5, yielding the solution (3, 5).
Solve the system: (x/2) + y = 7 and (x/2) - y = 3. What is the value of y?
2
1
4
3
Adding the two equations cancels y, leading to x = 10. Substituting x = 10 into one of the equations gives y = 2.
Solve the system: 2(x + y) = 12 and x - y = 2. What is the value of y?
2
4
3
1
Dividing the first equation gives x + y = 6. Adding it to the second equation cancels y, leading to x = 4 and subsequently y = 2.
Solve the system: 3x + 2y = 18 and x - y = 1. What is the value of x?
5
4
6
3
Expressing x from the second equation as x = y + 1 and substituting into the first yields 5y = 15, which leads to y = 3 and hence x = 4.
Solve the system: 7x + 3y = 31 and 7x - y = 27. What is the value of y?
1
3
0
2
Subtracting the second equation from the first cancels the x terms, resulting in 4y = 4, and therefore y = 1.
Solve the system: 2(x - y) = 4 and x + y = 10. What is the value of x?
7
5
6
8
Dividing the first equation gives x - y = 2. Adding it to x + y = 10 cancels y, resulting in 2x = 12 and thus x = 6.
Solve the system: 3(x + 2y) = 27 and 2x - y = 8. What is the value of y?
3
2
4
1
The first equation simplifies to x + 2y = 9, so x = 9 - 2y. Substituting into the second equation and solving yields y = 2.
Hard
Solve the system: 3x + 4y = 31 and 5x - 2y = 4. What is the ordered pair (x, y)?
(4, 11/2)
(3, 5)
(3, 6)
(3, 11/2)
Multiplying the second equation by 2 gives 10x - 4y = 8. Adding this to the first equation eliminates y, resulting in 13x = 39 and x = 3. Substituting back yields y = 11/2.
Solve the system: 2x + 3y = 17 and 4x - y = 11. What is the value of y?
11/7
25/7
23/7
17/3
Express y from the second equation as y = 4x - 11 and substitute into the first equation. Solving yields x = 25/7 and then y = 23/7.
Solve the system: 5x + 2y = 16 and 3x - 4y = -2. What is the value of x?
30/13
32/13
30/11
28/13
Multiplying the first equation by 2 gives 10x + 4y = 32. Adding this result to the second equation cancels y, leading to 13x = 30 and therefore x = 30/13.
Solve the system: x + y = 7, 2x + y = 10, and 3x + 2y = 17 using elimination. What is the value of x?
2
3
4
5
Subtracting the first equation from the second gives x = 3. Substituting back yields y = 4, and verification with the third equation confirms the solution.
A line passing through (2, 3) and parallel to the line x - 2y = -4 also satisfies 3x + y = 11. What is the value of x at their intersection?
11/7
14/7
18/7
16/7
A line parallel to x - 2y = -4 has the same slope and its equation through (2, 3) is y = (1/2)x + 2. Substituting this into 3x + y = 11 and solving gives x = 18/7.
1
2
3
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5
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7
8
9
10
11
12
13
14
15
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17
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20
0
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Study Outcomes

  1. Apply elimination methods to solve systems of equations accurately.
  2. Analyze multiple-choice questions to systematically discard incorrect options.
  3. Evaluate algebraic expressions to identify which steps lead to correct solutions.
  4. Integrate strategic thinking to improve problem-solving skills under test conditions.

Solving Systems Elimination Worksheet Cheat Sheet

  1. Master the elimination method - Dive into the classic elimination strategy where you add or subtract entire equations to zap one variable right off the page. It's like math magic: after elimination, you're left with a single-variable problem that's quick to solve. Grab more tips on this trick at Mathcation.
  2. Write equations in standard form - Get into the habit of rearranging each equation as Ax + By = C before you begin. Standard form creates a neat foundation for eliminating variables without extra fuss. Check out step-by-step guides at Green e Math.
  3. Spot coefficient pairs - Scan both equations to find coefficients you can transform into perfect opposites with minimal effort. Identifying these pairs is like tuning into secret frequencies that make elimination effortless. Learn how to spot them at BYJU's.
  4. Scale for success - Multiply one or both equations by strategic factors to line up those coefficients just right. Think of it as dialing in the exact volume so two equations seamlessly cancel out a variable. Find practice worksheets at OnlineMath4All.
  5. Solve the simplified equation - Once one variable is gone, you're left with a solo term to tackle. Plug in your arithmetic skills to find the value quickly and confidently. See clear examples at Algebra House.
  6. Back-substitute like a pro - After nailing one variable, drop that value back into one of the original equations to solve for the second. It's like backtracking a treasure map to the final X. Explore back-substitution tips at Albert.io.
  7. Verify your victory - Always plug both found values back into the original equations to confirm they check out. This double-check helps you catch sneaky errors before they cost you points. See verification strategies at Let's Make Math Simple.
  8. Handle special cases with ease - If elimination yields 0 = 0, you've stumbled on infinitely many solutions; if it gives 0 = 5, there's no solution at all. Recognizing these scenarios saves time and frustration during crunch time. Learn more at Mathcation.
  9. Mix up your practice problems - Challenge yourself with a variety of coefficient pairs and equation setups to build flexibility. The more systems you tackle, the sharper your elimination reflexes become. Get varied practice sets at Green e Math.
  10. Build consistent confidence - Like any skill, elimination shines with regular practice and a curious mindset. Keep at it, celebrate small victories, and soon you'll breeze through any system of equations. Stay motivated with resources from Albert.io.
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