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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

Algebra and Trigonometry (6th Edition)
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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**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
Transcribed Image Text:**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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