Simultaneous Linear Equations • Topic 3 of 3

Simple Word Problems Based on Linear Equations

What are Linear Equation Word Problems?

A linear equation word problem is a real-life scenario described in text description that can be translated into a mathematical pair of simultaneous equations. These problems occur in everyday settings such as shopping tallies, age differences, geometry dimensioning, fractions, or sports counting.

The process of solving word problems involves a systematic translation process:

  • Step 1: Identify the Unknowns: Pinpoint the two distinct unknown quantities the problem is asking you to find. Assign them a unique variable letter, usually x and y.
  • Step 2: Translate Sentences into Equations: Read the clues step-by-step. Words like "is" or "equal to" translate to an equals sign (\(=\)), while terms like "more than" map to addition (\(+\)) and "times" map to multiplication (\(\times\)).
  • Step 3: Solve the System: Choose whichever method you find easiest (Elimination, Substitution, or Cross-Multiplication) to compute the values of x and y.
  • Step 4: Answer Check: Verify that your answers make practical, logical sense within the original context of the real-world story.
Elimination MethodSolve: 2x + 3y = 13 ... (1) 5x − 2y = 4 ... (2)Step 1Multiply (1) by 2: 4x + 6y = 26Step 2Multiply (2) by 3: 15x − 6y = 12Step 3Add equations: 19x = 38 → x = 2Step 4Substitute x=2 in (1): 4+3y=13 → y=3Answerx = 2, y = 3Best used when: both variables have coefficients > 1Choose to eliminate the variable whose coefficients havethe smallest LCM — less arithmetic!
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Worked Example

Solve a standard problem on Simple Word Problems Based on Linear Equations.

Solution

Apply the formula/method shown in the concept section above.

Key Points

  • Understand the definition and properties of Simple Word Problems Based on Linear Equations.
  • Study the worked examples and practice similar problems.
  • Always verify your answer using the original conditions.
Tap an option to check your answer0 / 4
Q1.To solve a word problem, first define the:
Explanation: Define variables.
Q2."The sum of two numbers is $15$" gives:
Explanation: $x+y=15$.
Q3.The sum of two numbers is $20$ and their difference is $4$. The larger is:
Explanation: $(20+4)/2=12$.
Q4.To find two unknowns, you need how many equations?
Explanation: Two.