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Ch. 5 - Systems of Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
Chapter 6, Problem 48

In Exercises 47–48, solve each system by the method of your choice. (x - y)/3 = (x + y)/2 - 1/2 (x + 2)/2 - 4 = (y + 4)/3
Exercise 48: Two variable system of linear equations to solve.

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1
Step 1: Start by rewriting each equation to eliminate the fractions. For the first equation, multiply both sides by the least common denominator (LCD) of 3 and 2, which is 6, to clear the denominators.
Step 2: After multiplying, simplify the resulting equation by distributing and combining like terms. This will give you a linear equation in terms of x and y without fractions.
Step 3: For the second equation, multiply both sides by the LCD of 2 and 3, which is 6, to clear the denominators. Then simplify by distributing and combining like terms.
Step 4: Now you have a system of two linear equations without fractions. Use either substitution or elimination method to solve for x and y. For elimination, align the equations and add or subtract them to eliminate one variable.
Step 5: Once one variable is eliminated, solve for the remaining variable. Substitute this value back into one of the original simplified equations to find the value of the other variable.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Systems of Linear Equations

A system of linear equations consists of two or more linear equations with the same variables. The solution is the set of variable values that satisfy all equations simultaneously. Understanding how to interpret and manipulate these systems is essential for finding their solutions.
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Methods for Solving Systems

Common methods to solve systems include substitution, elimination, and graphing. Each method involves manipulating the equations to isolate variables or eliminate one variable, making it easier to find the solution. Choosing the appropriate method depends on the system's structure.
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Algebraic Manipulation and Simplification

Solving the given system requires careful algebraic manipulation, such as clearing denominators, combining like terms, and isolating variables. Simplifying complex fractions and expressions is crucial to transform the system into a more manageable form for solving.
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