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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} 2x + 2y & = & 8 \\ 7x -6y & = & 15 \end{eqnarray}\right.
  2. \left\{\begin{eqnarray} 4z + 4t & = & -8 \\ 7z + 12t & = & -24 \end{eqnarray}\right.
  3. \left\{\begin{eqnarray} -4x + 6y & = & -4 \\ 8x + 5y & = & -26 \end{eqnarray}\right.
  4. \left\{\begin{eqnarray} 4a + 6b & = & 14 \\ 12a + 5b & = & 29 \end{eqnarray}\right.

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

  5. \left\{\begin{eqnarray} 4x + 4y & = & 8 \\ 9x -5y & = & -24 \end{eqnarray}\right.
  6. \left\{\begin{eqnarray} 5z + 3t & = & 2 \\ 9z + 4t & = & 5 \end{eqnarray}\right.
  7. \left\{\begin{eqnarray} 7x -4y & = & -9 \\ 9x + 3y & = & -36 \end{eqnarray}\right.
  8. \left\{\begin{eqnarray} 4a -4b & = & -12 \\ 7a -5b & = & -19 \end{eqnarray}\right.

    9. five orange juices and four coffees cost £9.90 and three orange juices and five coffees cost £9.45.

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