LT

Test: Systems of linear equations

Dynamic tasks on solving and checking systems, determining the number of solutions and modelling word problems.

Question qty: 10
Duration in minutes: 20
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Sample questions

  • Does the pair (x, y) satisfy ax + by = c?
  • Solve the system: ax + by = c1 and ax − by = c2.
  • Solve the system: x + y = s and x − y = d.
  • How many solutions does the system ax + by = c and kax + kby = kc have?
  • Solve the system: x + y = s and 2x − y = t.
  • The solution of a system is written as the pair (x, y). What exactly does this mean?
  • A total of viso type A and B tickets were sold. An A ticket costs €a, a B ticket costs €b, and revenue was €suma. How many A and B tickets were sold? Give A first.

Systems of linear equations

A solution of a system is a pair of values satisfying both equations at the same time. Use elimination to cancel one variable, or substitution to express one variable in terms of the other.

Number of solutions and word problems

Intersecting lines give one solution, distinct parallel lines give none, and coincident lines give infinitely many. In a word problem, define both unknowns, translate the conditions into two equations and check the resulting pair in the original situation.

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