Explanation Given: The system of equations 3 x − y = 5 ; − 5 x + 2 y = − 10 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. We need to identify the x-intercept and y-intercept of the equation and plot the same to graph the system of equation and conclude the solution based on the below three cases. Case 1: When we get intersecting lines, 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 get coinciding lines, 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 have parallel lines, 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, slope will be SAME and y-intercept of the equation will be DIFFERENT. Here in this problem, we need to make use of the graphing utility to find the solution of the problem. The graph of system of equations 3 x − y = 5 and − 5 x + 2 y = − 10 is given below: Calculation: Description Solving equations 3 x − y = 5 → 1 s t e q u a t i o n − 5 x + 2 y = − 10 → 2 n d e q u a t i o n Step 1: Simplify the 1 s t equation to get the form of y = m x + b 3 x − y = 5 ⇒ − y = − 3 x + 5 ⇒ y = 3 x − 5 Step 2: Simplify the 2nd equation to get the form of y = m x + b − 5 x + 2 y = − 10 ⇒ 2 y = 5 x − 10 ⇒ y = 5 2 x − 10 2 ⇒ y = 5 2 x − 5 Step 3: Enter the first equation into Y1

6th Edition

ISBN: 2818440026546

Author: Blitzer

Publisher: PEARSON

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Chapter 4.1, Problem 77ES

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The solution of the given system of equation using graphing, 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 4.1, Problem 76ES

Chapter 4.1, Problem 78ES

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INTRO. AND INTERMEDIATE ALGEBRA FOR COL

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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