Explanation Procedure used: Solving linear systems by Addition: (1) If necessary, rewrite both equation in the form of A x + B y = C . (2) If necessary, multiply either equation or both equation by appropriate nonzero numbers so that the sum of the x- coefficient or the sum of the y- coefficients is 0. (3) Add the equation in step 2. The sum is an equation in one variable. (4) Solve the equation in one variable. (5) Back-substitute the value found in step 4 either of the given equations and solve for the other variable. (6) Check the solution in either of the original equations. Calculation: Consider the given equations. x + y = a (1) x − y = b (2) By using the above procedure, solve the system of equations. Step 1: The equations (1) and (2) are in the form A x + B y = C . Step 2: Let eliminate the term y. Since the coefficient of y term in both equations are opposite to each other, no need to multiply the equation. Step 3: Now add the equation (1) and (2) as follows. x + y = a x − y = b _ 2 x + 0 y = a + b Step 4: Solve the above equation. 2 x + 0 y = a + b 2 x 2 = a + b 2 [ Divide by 2 on both sides ] x = a + b 2 Step 5: Now, the x -coordinate of the solution is known. Back-substitute a + b 2 for x in the equations (1) and obtain the value of y

11th Edition

ISBN: 9780134758817

Author: SAUNDERS

Publisher: PEARSON CO

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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Chapter 11.1, Problem 10BE

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To solve: The system of equation x+y=a and x−y=b.

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Chapter 11.1, Problem 9BE

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The system of equation x + y = a and x − y = b .

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