Test
Systems of linear equations
Dynamic tasks on solving and checking systems, determining the number of solutions and modelling word problems.
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Sample questions
- Solve the system: x + y = ___ and x − y = ___.
- Does the pair (___, ___) satisfy ___x + ___y = ___?
- Solve the system: x + y = ___ and 2x − y = ___.
- Solve the system: ___x + ___y = ___ and ___x − ___y = ___.
- How many solutions does the system ___x + ___y = ___ and ___x + ___y = ___ have?
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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