Solve the following system for all solutions:2 + (y + 3)2 = 58-x +y = 1Two solutionsSubmit AnswerAnswer:andPrivacy Policy TermsCopyright 2021 DeltaMat.com

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College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter7: Systems Of Equations And Inequalities

Section7.1: Systems Of Linear Equations: Two Variables

Problem 5SE: Given a system of equations, explain at least two different methods of solving that system.

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Question

Solve the following system for all solutions:
2 + (y + 3)2 = 58
-x +y = 1
Two solutions
Submit Answer
Answer:
and
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Expert Solution

Step 1

Find $y$ in terms of $x$ from the equation $- x + y = 1$ .

$\begin{array}{rcl} - x + y & = & 1 \\ y & = & 1 + x \end{array}$

Substitute $y = 1 + x$ in the equation $x^{2} + {(y + 3)}^{2} = 58$ and simplify the equation .

$\begin{array}{rcl} x^{2} + {(y + 3)}^{2} & = & 58 \\ x^{2} + {(1 + x + 3)}^{2} & = & 58 \\ x^{2} + {(x + 4)}^{2} & = & 58 \\ x^{2} + x^{2} + 16 + 8 x & = & 58 \\ 2 x^{2} + 8 x + 16 - 58 & = & 0 \\ 2 x^{2} + 8 x - 42 & = & 0 \end{array}$

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