Discia GCSE Maths › Algebra › Solving Simultaneous Equations Graphically

Solving Simultaneous Equations Graphically worksheet

5 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

5 questions 13 marks Sheet 1
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  1. 2 marks

    The graphs of \(y = -x + 7\) and \(y = x + 1\) cross at the point \((3, 4)\).

    (a)

    Write down the solution of the simultaneous equations

    \(y = -x + 7\)

    \(y = x + 1\)

    (b)

    The graph of \(y = -3x + 13\) also passes through \((3, 4)\).

    Write down the solution of the simultaneous equations

    \(y = -x + 7\)

    \(y = -3x + 13\)

  2. 3 marks

    Omar is solving the simultaneous equations

    \(y = -x - 4\)

    \(y = 2x - 7\)

    by drawing both graphs. Omar says the graphs cross at \((1, -5)\).

    (a)

    Calculate the value of \(y\) given by \(y = -x - 4\) when \(x = 1\).

    (b)

    Calculate the value of \(y\) given by \(y = 2x - 7\) when \(x = 1\).

    (c)

    Is his answer right? Give a reason.

  3. 3 marks

    The graph of \(y = 2x + 8\) is drawn on the grid below.

    One straight line drawn on a coordinate grid, with room for a second-8-6-4-22468-10-9-8-7-6-5-4-3-2123456789100xy

    By drawing the graph of \(y = -x + 2\) on the same grid, solve the simultaneous equations

    \(y = 2x + 8\)

    \(y = -x + 2\)

  4. 2 marks

    The graphs of \(y = -x - 1\) and \(y = x - 7\) cross at the point \((3, -4)\).

    (a)

    Write down the solution of the simultaneous equations

    \(y = -x - 1\)

    \(y = x - 7\)

    (b)

    The graph of \(y = 3x - 13\) also passes through \((3, -4)\).

    Write down the solution of the simultaneous equations

    \(y = -x - 1\)

    \(y = 3x - 13\)

  5. 3 marks

    Leila is solving the simultaneous equations

    \(y = 2x - 11\)

    \(y = -3x + 9\)

    by drawing both graphs. Leila says the graphs cross at \((4, -3)\).

    (a)

    Work out the value of \(y\) given by \(y = 2x - 11\) when \(x = 4\).

    (b)

    Work out the value of \(y\) given by \(y = -3x + 9\) when \(x = 4\).

    (c)

    Is her answer right? Give a reason.

Answers

  1. (a) \(x = 3\), \(y = 4\)
    (b) \(x = 3\), \(y = 4\)
  2. (a) \(-5\)
    (b) \(-5\)
    (c) Yes — the point is on both graphs
  3. \(x = -2\), \(y = 4\)
  4. (a) \(x = 3\), \(y = -4\)
    (b) \(x = 3\), \(y = -4\)
  5. (a) \(-3\)
    (b) \(-3\)
    (c) Yes — the point is on both graphs

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