**Linear Equation Analysis****Objective:** Determine whether each given equation is linear in the variables $ x_1 $, $ x_2 $, and $ x_3 $.**Equations:****a.** $ x_1 + 5x_2 - \sqrt{2}x_3 = 1 $**b.** $ x_1 + 3x_2 + x_1x_3 = 2 $**c.** $ x_1 = -7x_2 + 3x_3 $**d.** $ x_1^{-2} + x_2 + 8x_3 = 5 $**e.** $ x_1^{3/5} - 2x_2 + x_3 = 4 $**f.** $ \pi x_1 - \sqrt{2}x_2 = 7^{1/3} $### Explanation:**a.** The equation $ x_1 + 5x_2 - \sqrt{2}x_3 = 1 $ is linear because it can be written in the form $ a_1x_1 + a_2x_2 + a_3x_3 + a_4 = 0 $, where $ a_1, a_2, a_3, $ and $ a_4 $ are constants.**b.** The equation $ x_1 + 3x_2 + x_1x_3 = 2 $ is not linear due to the presence of the product $ x_1x_3 $, which is nonlinear.**c.** The equation $ x_1 = -7x_2 + 3x_3 $ is linear because it can also be written as $ x_1 + 7x_2 - 3x_3 = 0 $.**d.** The equation $ x_1^{-2} + x_2 + 8x_3 = 5 $ is not linear since it includes the term $ x_1^{-2} $, which is nonlinear.**e.** The equation $ x_1^{3/5} - 2x_2 + x_3 = 4 $ is not linear because it involves the nonlinear term \( x_1^{3

Answered: Image /qna-images/answer/6604bd8c-4502-40b0-a943-8f812d4261e1.jpg

1. In each part, determine whether the equation is linear in. x2, and x3. a. x₂ + 5x₂ - √√2x₂ = 1 c. x₁ = -7x₂ + 3x3 e. x³/5 - 2x₂ + x3 = 4 b. x₁ + 3x₂ + x₁ x3 = 2 d. x² + x₂ + 8x3 = 5 f. πx₁ -√√2x₂ = 7¹/3

1. In each part, determine whether the equation is linear in. x2, and x3. a. x₂ + 5x₂ - √√2x₂ = 1 c. x₁ = -7x₂ + 3x3 e. x³/5 - 2x₂ + x3 = 4 b. x₁ + 3x₂ + x₁ x3 = 2 d. x² + x₂ + 8x3 = 5 f. πx₁ -√√2x₂ = 7¹/3

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter2: Functions And Graphs

Section2.4: Writing And Graphing Equations Of Lines

Problem 80E

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Question

**Linear Equation Analysis**

**Objective:**
Determine whether each given equation is linear in the variables $ x_1 $, $ x_2 $, and $ x_3 $.

**Equations:**

**a.** $ x_1 + 5x_2 - \sqrt{2}x_3 = 1 $

**b.** $ x_1 + 3x_2 + x_1x_3 = 2 $

**c.** $ x_1 = -7x_2 + 3x_3 $

**d.** $ x_1^{-2} + x_2 + 8x_3 = 5 $

**e.** $ x_1^{3/5} - 2x_2 + x_3 = 4 $

**f.** $ \pi x_1 - \sqrt{2}x_2 = 7^{1/3} $

### Explanation:

**a.** The equation $ x_1 + 5x_2 - \sqrt{2}x_3 = 1 $ is linear because it can be written in the form $ a_1x_1 + a_2x_2 + a_3x_3 + a_4 = 0 $, where $ a_1, a_2, a_3, $ and $ a_4 $ are constants.

**b.** The equation $ x_1 + 3x_2 + x_1x_3 = 2 $ is not linear due to the presence of the product $ x_1x_3 $, which is nonlinear.

**c.** The equation $ x_1 = -7x_2 + 3x_3 $ is linear because it can also be written as $ x_1 + 7x_2 - 3x_3 = 0 $.

**d.** The equation $ x_1^{-2} + x_2 + 8x_3 = 5 $ is not linear since it includes the term $ x_1^{-2} $, which is nonlinear.

**e.** The equation $ x_1^{3/5} - 2x_2 + x_3 = 4 $ is not linear because it involves the nonlinear term \( x_1^{3

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