T2.4.4 Simultaneous solutions from graphs Quiz: KS3 Maths, Unit 2

The 20 questions

1. Lines y = x + 1 and y = 3 - x cross at (1, 2). What is the solution to the simultaneous equations?

   • x = 1, y = 2
   • x = 1, y = 4
   • x = 0, y = 3
   • x = 2, y = 1

2. Two straight lines have the same gradient but different y-intercepts. How many points do they share?

   • Infinitely many
   • One
   • None
   • Two

3. Two equations give exactly the same straight line. How many solutions do they have?

   • None at all
   • Exactly one solution
   • Infinitely many
   • Exactly two solutions

4. Lines y = 2x and y = x + 3 cross at (3, 6). What is the solution to the simultaneous equations?

   • x = 2, y = 4
   • x = 6, y = 3
   • x = 3, y = 3
   • x = 3, y = 6

5. Which pair satisfies both x + y = 3 and y = x - 1?

   • (2, 1)
   • (0, 3)
   • (3, 0)
   • (1, 2)

6. A pen and a ruler cost £5 altogether. The pen costs £2 more than the ruler. What is the cost of each?

   • Pen £4, ruler £1
   • Pen £3.50, ruler £1.50
   • Pen £2.50, ruler £2.50
   • Pen £3, ruler £2

7. Where do the graphs of y = x² and y = x meet?

   • (0, 0) and (1, 1)
   • (0, 1) and (1, 0)
   • (1, 1) only
   • (0, 0) and (-1, -1)

8. Solve the simultaneous equations y = 2x + 1 and y = -x + 7.

   • x = 3, y = 7
   • x = 2, y = 3
   • x = 2, y = 5
   • x = 5, y = 2

9. What do the coordinates of an intersection point of two graphs represent?

   • The gradient shared by both lines
   • The total of the two y-intercepts
   • The point where either line crosses an axis
   • The x and y values that satisfy both equations

10. Solve the simultaneous equations x + 2y = 8 and x = 2.

    • (8, 0)
    • (3, 2)
    • (2, 6)
    • (2, 3)

11. Where do the lines y = x and y = 6 - x meet?

    • (6, 0)
    • (3, 3)
    • (2, 4)
    • (0, 6)

12. Solve the simultaneous equations 2x + y = 10 and x - y = 2.

    • x = 3, y = 4
    • x = 4, y = 2
    • x = 2, y = 6
    • x = 6, y = -2

13. A straight line and a curve cross at two points on a graph. How many solutions does the pair of equations have?

    • Two
    • None
    • Three
    • One

14. Taxi A charges £5 plus £1 per mile. Taxi B charges £2 plus £2 per mile. After how many miles do they cost the same?

    • 3 miles
    • 2 miles
    • 7 miles
    • 5 miles

15. Where do the lines y = 4 and y = 2x - 2 meet?

    • (3, 2)
    • (2, 4)
    • (4, 3)
    • (3, 4)

16. Which situation means two straight lines are parallel and never meet?

    • Same gradient and different y-intercepts
    • Different gradients and different y-intercepts
    • Different gradients
    • Same y-intercept and different gradients

17. Where do the lines x + y = 6 and x - y = 2 meet?

    • (2, 4)
    • (4, 2)
    • (4, 6)
    • (6, 2)

18. Where do the graph y = x² - 2 and the line y = 2 meet?

    • (2, 0) and (-2, 0)
    • (4, 2) only
    • (-2, 2) and (2, 2)
    • (-2, 0) and (2, 2)

19. Solve 3x + 2y = 12 and y = 3 simultaneously. What is x?

    • x = 2
    • x = 3
    • x = 4
    • x = 6

20. How many points do two straight lines with different gradients have in common?

    • Exactly two
    • None
    • Exactly one
    • Infinitely many

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