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Exploring Systems of Linear Equations in Two Variables

This document delves into systems of linear equations involving two variables, presenting key scenarios: one solution, no solution, or infinitely many solutions. The classification of these systems as consistent or inconsistent, and dependent or independent, is explained in detail. Examples are provided to solve and classify equations. Practical applications include rowing speed calculations in river conditions and alcohol mixture problems, demonstrating real-world uses of linear equations. Understand how to analyze and classify linear systems effectively.

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Exploring Systems of Linear Equations in Two Variables

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  1. 9.2 Systems of Linear Equations (2 variables)

  2. For a system of linear equations in two variables, exactly one of the following is true. • The system has exactly one solution. • The system has NO solution. • The system has infinitely many solutions.

  3. No solution – inconsistent • Has a solution – consistent • Dependent – infinitely many solutions • Independent – one solution

  4. Solve and classify 4x – y = 0 5x + 2y = 52

  5. Solve and classify 12x – 3y = 7 -20x + 5y = 4

  6. A woman rows a boat upstream from one point on a river to another point 7 miles away in an hour and 15 minutes. The return trip, traveling with the current, takes only 50 minutes. How fast does she row relative to the water (in mph) and what is the speed of the current?

  7. A vintner fortifies wine that contains 10% alcohol by adding a 60% alcohol solution to it. The resulting mixture has an alcohol strength of 12% and fills 1100 one-liter bottles. How many liters of the wine and of the alcohol solution does he use?

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