English

System of Equations (Word Problems)

🎯 Learning Goals

  • Translate complex word problems into a system of two equations
  • Identify the two unknown quantities and define them as x and y

💡 Why Learn This?

Word problems involving systems of equations are practical. They allow you to figure out individual prices when only totals are known, or determine optimal mixtures of different ingredients in chemistry or cooking.

Building Equations from Text

The key to solving word problems is replacing the unknown values with 'x' and 'y', and creating two distinct equations based on the conditions given.

{
x + y = 52x - y = 1

Example: Shopping

  • 2 apples and 3 oranges cost 400 yen.
  • 4 apples and 1 orange cost 500 yen.

⚠️ Common Pitfalls

Be careful not to mix up the variables! If x is the price of an adult ticket and y is the child ticket, make sure you don't accidentally multiply the adult count by y. Always label what x and y represent.

Interactive Simulator

Read the problem, define x and y, and complete the equations.

[Problem] Admission to a park is 4000 yen for 2 adults and 3 children, and 3500 yen for 1 adult and 4 children.

Step 1: Define x and y

x =
y =

Step 2: Build the equations

Eq 1 (2 Adults, 3 Children):x +y =
Eq 2 (1 Adult, 4 Children):x +y =

📝 Summary & Recap

  • First, clearly define what 'x' and 'y' represent in the context of the problem.
  • Second, find two independent conditions in the text and translate each into an equation.

Quick Drill

Choose the correct equation for the sentence!

Equation for 'x apples and y oranges make 5 in total'?

🔍 Deep Dive (Optional)

In ancient times before algebra, people solved these types of problems using logic and trial-and-error, a method called the 'rule of false position'. Algebra gives us a direct and foolproof way to find the answer!

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