Systems of equations as models of word problems
Translate problems about motion, work, digits and rectangles into equations: name the unknowns x and y, write the system, solve it and check that the answer fits the story. This follows the Ukrainian Year 9 algebra book, section 14.
- Germany: grade 8
- Palestine: grade 11
- Ukraine: grade 9
- Russia: grade 7
Guide
In the Ukrainian Year 9 algebra book (section 14, "A system of two equations in two variables as a mathematical model of an applied problem") a real-life problem is "translated" into the language of mathematics: expressions, equations, systems. The result of the translation is called a mathematical model, and the problem itself is an applied problem.
The solution has four steps, as in the book. 1) "Let the speed of the first hiker be x km/h and of the second y km/h": name the unknowns. 2) Write one equation for each condition; together they form a system. 3) Solve the system, for example by substitution. 4) Check that the answer fits the story: a speed cannot be negative and a digit cannot be a fraction. Write the "Answer".
In this studio you do not type the system into cells. The first equation of the system has been solved for y in terms of x (as the book does when substituting), and the last column tests the second condition. Change x until the last column matches the condition.
The "why" question asks you to explain why a number is not a solution of the problem.