Systems from word problems

Systems from word problems

Systems from word problems

Many real problems have two unknowns linked by two facts. You can write one equation for each fact and solve the system.

A worked example

"The sum of two numbers is 11 and their difference is 3. Find the numbers."

Let the larger number be x and the smaller be y. The two facts give:

x + y = 11

x − y = 3

Add the equations: 2x = 14, so x = 7. Then y = 11 − 7 = 4. The numbers are 7 and 4.

How to set one up

  • Name each unknown with a letter.
  • Turn each sentence or fact into one equation.
  • Solve by substitution or elimination, then check the answer makes sense in the story.

Three rules that always help

  • One unknown per letter, one equation per fact.
  • Two unknowns usually need two equations.
  • Check the answer against the words, not just the algebra.

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