Explanation Given: The system of equation 2 ( x − 1 ) − y = − 3 ; y = 2 x + 3 Solving a system of equation means finding the value of (x, y) which will make both the equation true. There are different types of solution for system of equation. Case 1: When we end up the value of x and y, the solution of system of equations is UNIQUE and it is the point where the graphs intersect. The solution set in interval notation is given by { ( x , y ) } . The solution is described as consistent and independent. Also for intersecting lines, the slope of the system of equations will be different. Case 2: When we end up with an IDENTITY equation, the solution of system of equations is INFINITE because the lines meet at numerous points. The solution is represented as { x ∈ ℜ , y ∈ ℜ } The solution is described as consistent and dependent. Also for intersecting lines, the slope and y-intercept of the system of equations will be same. Case 3: When we end up with a CONDRADICTING equation, the solution of the system of equations is NO SOLUTION because the lines will never meet. The solution is represented as { } or ∅ . The system of equation hence described as inconsistent. Also for parallel lines, have same slope but y-intercept of the equation will be different. If any one of the system of equation involve fractions, get rid of the fraction by multiplying the LCD throughout the equation. We need to select one equation and solve it for one of its variables. In the other equation, substitute for the variable just solved. Solve the new equation. Substitute the values found into any equation involving both variables and solve for the other variable. Calculation: Description Solving equations 2 ( x − 1 ) − y = − 3 ; y = 2 x + 3 Step 1: If any one of the system of equation involve fractions, get rid of the fraction by multiplying the LCD throughout the equation

Introductory and Intermediate Algebra for College Students (5th Edition)

5th Edition

ISBN: 9780134178141

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 4.2, Problem 21ES

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The solution of the given system of equation using substitution method, check if the system is no solution or an infinite number of solutions and express solution set in interval notation.

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Chapter 4.2, Problem 20ES

Chapter 4.2, Problem 22ES

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Introductory and Intermediate Algebra for College Students (5th Edition)

Ch. 4.1 - Prob. 1CAVC Ch. 4.1 - Prob. 2CAVC Ch. 4.1 - Prob. 3CAVC Ch. 4.1 - Prob. 4CAVC Ch. 4.1 - Prob. 1ES Ch. 4.1 - Prob. 2ES Ch. 4.1 - Prob. 3ES Ch. 4.1 - Prob. 4ES Ch. 4.1 - Prob. 5ES Ch. 4.1 - Prob. 6ES

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