Explanation Given Information: Provided equations are, y = x + 1 , x 2 + y 2 = 1 . Formula used: Following steps are used for solving the system of equations by using substitution method. Step 1: Solve one equation for one variable. Step 2: Substitute the value of variable from step 1 to the other equation. Step 3: Solve new equation for specified variable. Step 4: Make factors of the resulting equation and simplify by applying zero product rule on factors as: Assume a and b are two real numbers: If ( a + b ) ( a − b ) = 0 Then, ( a + b ) = 0 or ( a − b ) = 0 Calculation: Consider the system of equations y = x + 1 , x 2 + y 2 = 1 . Take equation y = x + 1 among these and write it in terms of one variable: y = x + 1 Now substitute y = x + 1 into the other equation x 2 + y 2 = 1 : x 2 + ( x + 1 ) 2 = 1 Now, subtract 1 from both sides: x 2 + ( x + 1 ) 2 − 1 = 1 − 1 x 2 + x 2 + 1 + 2 x − 1 = 0 2 x 2 + 2 x = 0 Now, solve this quadratic equation by factoring, 2 x ( x + 1 ) = 0 Apply zero product rule on above factors: 2 x = 0 or ( x + 1 ) = 0 If 2 x = 0 Then, x = 0 Or, if ( x + 1 ) = 0 Then, x = − 1 Thus, values of x here are 0 and − 1 . Now, substitute these values in y = x + 1 . For x = 0 , substitute x = 0 in y = x + 1 : y = x + 1 = 0 + 1 = 1 And, For x = − 1 , substitute x = − 1 in y = x + 1 : y = x + 1 = − 1 + 1 = 0 The solution set is { ( 0 , 1 ) , ( − 1 , 0 ) } Graph: For graph, consider the system of given equations y = x + 1 , x 2 + y 2 = 1 . For equation y = x + 1 : For x = − 5 Substitute x = − 5 in y = x + 1 : y = x + 1 y = − 5 + 1 y = − 4 For x = − 3 Substitute x = − 3 in y = x + 1 : y = x + 1 y = − 3 + 1 y = − 2 For x = 0 Substitute x = 0 in y = x + 1 : y = x + 1 y = 0 + 1 y = 1 For x = 2 Substitute x = 2 in y = x + 1 : y = x + 1 y = 2 + 1 y = 3 Table of above observations for y = x + 1 : x − 5 − 3 0 2 y − 4 − 2 1 3 For equation x 2 + y 2 = 1

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ISBN: 9781266148941

Author: Miller

Publisher: MCG CUSTOM

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Chapter 13.4, Problem 11PE

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To calculate: The solution of the equations y=x+1,x2+y2=1 by using substitution method. Also draw the graph of this given system of equations.

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Chapter 13.4, Problem 10PE

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The solution of the equations y = x + 1 , x 2 + y 2 = 1 by using substitution method. Also draw the graph of this given system of equations.

Solution Summary: The author explains the steps used to solve the system of equations by using substitution method.

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To calculate: The solution of the equations y=x+1,x2+y2=1 by using substitution method. Also draw the graph of this given system of equations.

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