Explanation Given: The system of equation 2 x − y = 3 ; 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. 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 − y = 3 ; 5 x − 2 y = 10 Step 1: If any one of the system of equation involve fractions, get rid of the fraction by multiplying the LCD throughout the equation. And write the simplified equation as 1 s t and 2 n d equation. In this problem it is already in simplified form. If needed we need select one equation and solve it for one of its variables y = 2 x − 3 → 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 2: Substitute the 1 s t equation into the 2 n d equation

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ISBN: 9781323566961

Author: Blitzer

Publisher: PEARSON C

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Chapter 4.2, Problem 9ES

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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 8ES

Chapter 4.2, Problem 10ES

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