LT

Test: Systems of equations

This test covers systems containing linear, quadratic and rational equations. Students use substitution or elimination, verify ordered pairs and interpret the meaning of a solution both algebraically and graphically.

Question qty: 10
Duration in minutes: 19
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Sample questions

  • Find x and y if x + y = s and xy = p. Give both numbers.
  • What do solutions of a two-equation system mean graphically?
  • Solve x + y = s and x − y = d.
  • How many ordered pairs (x, y) satisfy x + y = s and xy = p?
  • The system is y = x² and x = x. Find the solution pair.
  • Solve x + y = s and x/y = q.
  • Does (x, y) satisfy x + y = s and xy = p?
  • One equation is already y = x² + 1. Which method is most convenient to start with?

Systems of equations

A solution of a system must satisfy every equation simultaneously. Substitution is convenient when one variable is easy to isolate, while elimination works well when coefficients can be matched to cancel a variable.

Non-linear systems

A quadratic or other non-linear equation may produce several values for one variable. Find the corresponding second value for each one and check ordered pairs. Graphically, solutions are the common intersection points of all equations.

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