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QMMaths

Simultaneous equations (2)

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In this sheet you should write your answers separated by commas. E.g. x=1, y=3.

    Solve the following pairs of simultaneous equations. You may need to multiply one equation first.

  1. \left\{\begin{eqnarray} 3x + 3y & = & -3 \\ 8x -9y & = & 26 \end{eqnarray}\right.
  2. \left\{\begin{eqnarray} 5z + 3t & = & 1 \\ 8z + 6t & = & -2 \end{eqnarray}\right.
  3. \left\{\begin{eqnarray} -3x + 9y & = & 9 \\ 6x + 7y & = & -18 \end{eqnarray}\right.
  4. \left\{\begin{eqnarray} 3a + 5b & = & -7 \\ 6a + 2b & = & 2 \end{eqnarray}\right.

    5. Solve the following pairs of simultaneous equations. You will need to multiply both equations first.

  5. \left\{\begin{eqnarray} 8x + 2y & = & -10 \\ 3x -3y & = & -15 \end{eqnarray}\right.
  6. \left\{\begin{eqnarray} 7z + 4t & = & 0 \\ 9z + 5t & = & 0 \end{eqnarray}\right.
  7. \left\{\begin{eqnarray} 9x -4y & = & -31 \\ 4x + 5y & = & -7 \end{eqnarray}\right.
  8. \left\{\begin{eqnarray} 5a -2b & = & 1 \\ 2a -5b & = & -8 \end{eqnarray}\right.

    9. four orange juices and five coffees cost £10.30 and three orange juices and four coffees cost £8.05.

  9. What is the price of a coffee?
  10. What is the price of an orange juice?