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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 + 3y & = & -5 \\ 7x -6y & = & 32 \end{eqnarray}\right.
  2. \left\{\begin{eqnarray} 2z + 3t & = & 5 \\ 5z + 6t & = & 11 \end{eqnarray}\right.
  3. \left\{\begin{eqnarray} -4x + 5y & = & 9 \\ 12x + 6y & = & -6 \end{eqnarray}\right.
  4. \left\{\begin{eqnarray} 4a + 8b & = & 8 \\ 8a + 3b & = & 16 \end{eqnarray}\right.

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

  5. \left\{\begin{eqnarray} 8x + 3y & = & 9 \\ 7x -4y & = & -12 \end{eqnarray}\right.
  6. \left\{\begin{eqnarray} 4z + 4t & = & 0 \\ 5z + 5t & = & 0 \end{eqnarray}\right.
  7. \left\{\begin{eqnarray} 4x -2y & = & 18 \\ 3x + 5y & = & -6 \end{eqnarray}\right.
  8. \left\{\begin{eqnarray} 6a -2b & = & -4 \\ 5a -3b & = & -2 \end{eqnarray}\right.

    9. five orange juices and four coffees cost £9.40 and three orange juices and five coffees cost £9.15.

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