[discia] GCSE Maths › Algebra › Simultaneous Equations

Simultaneous Equations

discia.org 10 questions · 38 marks
Name Date
  1. Either paper 3 marks

    Solve these simultaneous equations.

    \(4x + 5y = 39\)

    \(4x - 5y = -31\)

    Show answer
    \(x = 1\), \(y = 7\)
    Another like this
  2. Either paper 3 marks

    Solve the simultaneous equations

    \(y = 2x + 6\)

    \(4x + 3y = 48\)

    Show answer
    \(x = 3\), \(y = 12\)
    Another like this
  3. Either paper 3 marks

    \(x = 3\) and \(y = 8\) is the solution of the simultaneous equations

    \(6x + ay = 34\)

    \(x - 5y = -37\)

    Calculate the value of \(a\).

    Show answer
    \(2\)
    Another like this
  4. Either paper 3 marks

    Solve these simultaneous equations.

    \(5x + 6y = 18\)

    \(5x + 2y = 26\)

    Show answer
    \(x = 6\), \(y = -2\)
    Another like this
  5. Either paper 4 marks

    Solve the simultaneous equations

    \(5x + 4y = -11\)

    \(7x + 12y = -9\)

    Show answer
    \(x = -3\), \(y = 1\)
    Another like this
  6. Either paper 4 marks

    A stationery shop sells folders and notepads.

    3 folders and 5 notepads cost £52 altogether.

    9 folders and 2 notepads cost £91 altogether.

    Calculate the cost of one folder and the cost of one notepad.

    Show answer
    One folder costs £9 and one notepad costs £5.
    Another like this
  7. Either paper 4 marks

    Here are two simultaneous equations.

    \(3x = 12 - 4y\)

    \(5x - 4y = -44\)

    (a)

    Write the first equation in the form \(ax + by = c\).

    (b)

    Solve the simultaneous equations.

    Show answer
    (a) \(3x + 4y = 12\)
    (b) \(x = -4\), \(y = 6\)
    Another like this
  8. Either paper 5 marks

    A plumber charges a fixed call-out fee and then the same amount for every hour of work.

    A job that takes 4 hours costs £203.

    A job that takes 6 hours costs £291.

    (a)

    Calculate the call-out fee and the amount charged for each hour.

    (b)

    Work out the cost of a job that takes 9 hours.

    Show answer
    (a) The call-out fee is £27 and the charge for each hour is £44.
    (b) \(\text{£}423\)
    Another like this
  9. Either paper 4 marks

    A car park charges £4 for a car and £6 for a van.

    One day there were 38 vehicles in the car park, and the total charge was £196.

    Work out how many cars and how many vans there were.

    Show answer
    There were 16 cars and 22 vans.
    Another like this
  10. Either paper 5 marks

    In a coding club, there are \(x\) boys and \(y\) girls.

    If 6 more boys and 14 more girls join, there would be half as many boys as girls.

    (a)

    Show that \(y = 2x - 2\)

    (b)

    If instead 12 more boys and 2 more girls join the coding club, there would be the same number of boys and girls.

    Work out the value of \(x\) and the value of \(y\).

    Show answer
    (a) \(x + 6 = \frac{ y + 14 }{2}\), which rearranges to \(y = 2x - 2\)
    (b) \(x = 12\) and \(y = 22\)
    Another like this
discia.org Simultaneous Equations · sheet 1
Answers Simultaneous Equations · sheet 1
  1. \(x = 1\), \(y = 7\)
  2. \(x = 3\), \(y = 12\)
  3. \(2\)
  4. \(x = 6\), \(y = -2\)
  5. \(x = -3\), \(y = 1\)
  6. One folder costs £9 and one notepad costs £5.
  7. (a) \(3x + 4y = 12\)
    (b) \(x = -4\), \(y = 6\)
  8. (a) The call-out fee is £27 and the charge for each hour is £44.
    (b) \(\text{£}423\)
  9. There were 16 cars and 22 vans.
  10. (a) \(x + 6 = \frac{ y + 14 }{2}\), which rearranges to \(y = 2x - 2\)
    (b) \(x = 12\) and \(y = 22\)
discia.org Simultaneous Equations · sheet 1