### Solving a System of Equations by TableTo 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 ValuesBelow 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.

Answered: Image /qna-images/answer/f1080a04-6dd2-4bee-8685-5f89ec95da16.jpg

Answered: Solve the system by table X -5 -4 Y₁…

Solve the system by table X -5 -4 Y₁ -3.5 -1.5 -2 -2 -.5 -2.5 1 -3 for some x, same y value the ordered pair (-4,-2) works in both equation -3 -2 3 2x+4 y = - = - x² Y₂ 2 x-4

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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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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