2.4.1 Simultaneous equations in two variables Quiz: Pearson Edexcel Maths, Unit 2

The 20 questions

1. How many independent linear equations are required to find a unique solution for two variables?

   • 2
   • 4
   • 1
   • 3

2. Which algebraic method eliminates one variable by adding or subtracting two equations?

   • Factorisation
   • Elimination
   • Substitution
   • Completing the square

3. Which algebraic method involves rearranging one equation to replace a variable in the other?

   • Substitution
   • Iteration
   • Elimination
   • Integration

4. Geometrically, what does a system of two linear equations in two variables represent?

   • Two straight lines
   • A circle and a line
   • A quadratic curve
   • Two parallel planes

5. When two distinct lines in a simultaneous system are parallel and non-intersecting, how many solutions exist?

   • Two
   • Infinitely many
   • One
   • Zero

6. When two simultaneous linear equations represent the exact same line, how many solutions exist?

   • Infinitely many
   • Two
   • Zero
   • One

7. What is the primary algebraic technique used to solve a simultaneous system of one linear and one quadratic equation?

   • Long division
   • Elimination
   • Integration
   • Substitution

8. Solving a simultaneous linear and quadratic equation typically results in a single equation in how many variables?

   • 1
   • 3
   • 2
   • 4

9. Solve for x in the simultaneous equations: x + y = 7 and x - y = 3.

   • 2
   • 7
   • 5
   • 10

10. Solve for y in the simultaneous equations: x + y = 7 and x - y = 3.

    • 3
    • 5
    • 2
    • 7

11. Solve for x in the simultaneous equations: 2x + y = 10 and x = 3.

    • 2
    • 4
    • 3
    • 10

12. Solve for y in the simultaneous equations: 2x + y = 10 and x = 3.

    • 3
    • 7
    • 4
    • 6

13. Find the x-coordinate of the intersection of y = x^2 and y = 2x.

    • 1
    • 2
    • 4
    • 0

14. What is the maximum number of intersection points possible between a straight line and a circle?

    • 1
    • 0
    • 2
    • 3

15. When solving a quadratic simultaneous equation yields a discriminant equal to zero, how many real solution pairs exist?

    • 2
    • 0
    • 4
    • 1

16. If the discriminant of the quadratic formed by substitution is negative, how many real solution pairs exist?

    • 2
    • Infinitely many
    • 0
    • 1

17. Solve for x: 3x + 2y = 12 and 3x - 2y = 6.

    • 3
    • 1.5
    • 6
    • 2

18. Solve for y: 3x + 2y = 12 and 3x - 2y = 6.

    • 3
    • 9
    • 1.5
    • 4.5

19. What algebraic term describes a set of simultaneous equations that has no solutions at all?

    • Homogeneous
    • Dependent
    • Inconsistent
    • Quadratic

20. What algebraic term describes a set of simultaneous equations with infinitely many solutions?

    • Dependent system
    • Inconsistent system
    • Quadratic system
    • Independent system

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