Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question
### Solving a System of Equations by Table To solve the system of equations using a table, consider the following two equations: 1. \( y = \frac{3}{2}x + 4 \) 2. \( y = -\frac{1}{2}x - 4 \) #### Table of Values Below is a table with selected values of \( x \), and their corresponding \( y \) values from both equations: | \( x \) | \( Y_1 \) | \( Y_2 \) | |--------|------|------| | -5 | -3.5 | -1.5 | | -4 | -2 | -2 | | -3 | -0.5 | -2.5 | | -2 | 1 | -3 | #### Explanation - **Find a common \( y \)-value**: Look for the \( x \) where both \( y_1 \) and \( y_2 \) have the same value. - In the table, when \( x = -4 \), both \( y_1 \) and \( y_2 \) equal \(-2\). Thus, the ordered pair \((-4, -2)\) is a solution that works for both equations in the system.
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Transcribed Image Text:### Solving a System of Equations by Table To solve the system of equations using a table, consider the following two equations: 1. \( y = \frac{3}{2}x + 4 \) 2. \( y = -\frac{1}{2}x - 4 \) #### Table of Values Below is a table with selected values of \( x \), and their corresponding \( y \) values from both equations: | \( x \) | \( Y_1 \) | \( Y_2 \) | |--------|------|------| | -5 | -3.5 | -1.5 | | -4 | -2 | -2 | | -3 | -0.5 | -2.5 | | -2 | 1 | -3 | #### Explanation - **Find a common \( y \)-value**: Look for the \( x \) where both \( y_1 \) and \( y_2 \) have the same value. - In the table, when \( x = -4 \), both \( y_1 \) and \( y_2 \) equal \(-2\). Thus, the ordered pair \((-4, -2)\) is a solution that works for both equations in the system.
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