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Pairs of Equations

Many practical problems involve finding a solution to a set of equations. This section introduces methods for finding solutions for pairs of linear equations and has applications in economics, engineering, science, agriculture, etc.

Try the following questions to refresh your memory and check your skills. If you have any difficulty follow the underlined links for further information.

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Full Answers

Self-Test

Questions
1. Draw the graphs of the lines \[ \begin{array}{lcl} 2x + \phantom{3}y & = & 5 \\ 2x + 3y & = & 7 \end{array} \] and estimate the point of intersection. Check your answer.

  See  Introduction
2. Solve the system of equations below by the substitution method.

\[ \begin{array}{rcl} v & = & 3u + 4 \\ u + v & = & 12 \end{array} \]

  See  Substitution
3. Solve the system of equations below by the elimination method.

\[ \begin{array}{lcl} 4A + 3B & = & 24 \\ 3A - \phantom{4}B & = & 5 \end{array} \]

  See  Elimination
4. Does a pair of simultaneous linear equations always have a solution?

  See  Introduction