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Quiz Chapter 3: Systems of Equations

10 questions · Form 4 Additional Mathematics Bab 3: Systems of Equations

10 questions · plays in fullscreen

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. If x - y = 3 and x² + y² = 29, find the value of xy.

  1. 10
  2. 20
  3. 12
  4. 15
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Answer: A

Square (x - y = 3): (x - y)² = 9 => x² - 2xy + y² = 9. Substitute x² + y² = 29: 29 - 2xy = 9 => 2xy = 20 => xy = 10.

2. When solving simultaneous equations involving one linear and one non-linear equation, what is the best first step?

  1. Differentiate the non-linear equation
  2. Express one variable in terms of another using the linear equation
  3. Square both equations
  4. Set the discriminant of the non-linear equation to zero
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Answer: B

The standard substitution method requires expressing one variable as the subject from the linear equation first, then substituting it into the non-linear equation.

3. If three planes in 3D space intersect along a common straight line, how many solutions does the system of three linear equations have?

  1. Exactly one solution
  2. No solution
  3. Infinitely many solutions
  4. Exactly three solutions
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Answer: C

When three planes intersect along a line, every point on that line is a common solution, resulting in infinitely many solutions.

4. In a system of three linear equations, if elimination leads to the statement 0 = 5, what does this indicate about the system?

  1. The system has five unique solutions
  2. The system has infinite solutions
  3. The system has no solution
  4. The system has x = 0 and y = 5
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Answer: C

An impossible identity such as 0 = 5 indicates a contradiction, meaning the planes do not share any common point of intersection, so there is no solution.

5. Geometrically, what does a single linear equation in three variables ax + by + cz = d represent?

  1. A straight line in 2D
  2. A plane in 3D space
  3. A sphere in 3D space
  4. A point in 3D space
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Answer: B

In 3D Cartesian coordinates, a first-degree linear equation in three variables represents a flat 2D plane.

6. Given x + 2y - z = 4, 2x - y + z = 3, and 3x + y + 2z = 11, calculate the value of z.

  1. z = 1
  2. z = 2
  3. z = -1
  4. z = 3
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Answer: B

Solving this system gives x = 1, y = 2, z = 2.

7. The perimeter of a rectangular garden is 28 m and its area is 40 m². Find the length and width of the garden.

  1. 10 m and 4 m
  2. 8 m and 5 m
  3. 14 m and 2 m
  4. 20 m and 2 m
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Answer: A

Let length = x, width = y. 2(x + y) = 28 => x + y = 14 => y = 14 - x. Area: xy = 40 => x(14 - x) = 40 => x² - 14x + 40 = 0 => (x - 10)(x - 4) = 0. Dimensions are 10 m and 4 m.

8. Solve the non-linear system: x - 2y = 1 and x² - 4y² = 5. Find x + 2y.

  1. 5
  2. 1
  3. 25
  4. 3
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Answer: A

Use difference of squares: x² - 4y² = (x - 2y)(x + 2y) = 5. Given x - 2y = 1, we get 1(x + 2y) = 5 => x + 2y = 5.

9. If elimination yields the identity 0 = 0 when solving a system of three linear equations, what can be concluded?

  1. There is no solution
  2. There are infinitely many solutions
  3. There is a single solution at (0, 0, 0)
  4. The variables are all equal to zero
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Answer: B

A tautology such as 0 = 0 signifies dependent equations, meaning the planes intersect along a line or coincide, giving infinitely many solutions.

10. Which of the following equations is a linear equation in three variables?

  1. 2x + 3y - z² = 5
  2. xy + z = 4
  3. 3x - 4y + 2z = 9
  4. 1x + y - 2z = 0
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Answer: C

A linear equation in three variables must have each variable raised to the power of 1 without product terms like xy. Thus, 3x - 4y + 2z = 9 is linear.

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