Translating a Two-Number Word Problem into a System of Equations
Apply Steps 1 through 4 of the problem-solving strategy for systems of linear equations to set up (but not solve) a system from a number problem.
Problem: The sum of two numbers is negative fourteen. One number is four less than the other. Find the numbers.
- Read the problem carefully.
- Identify what to find: two numbers.
- Name the unknowns using two variables: Let = one number and = the second number.
- Translate each verbal statement into its own equation. "The sum of two numbers is negative fourteen" becomes . "One number is four less than the other" becomes . The resulting system is:
This example isolates the translation step to show the key advantage of using a system of equations: each sentence in the problem maps directly to one equation, and each unknown gets its own variable. Compare this with the single-variable approach to the same problem, where both unknowns must be expressed through a single variable before writing a single equation — many learners find the two-variable setup more straightforward because the variable assignments are simpler.
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Ch.5 Systems of Linear Equations - Elementary Algebra @ OpenStax
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