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Find the point (x₁,x2) that lies on the line x₁ + 3x2 = 13 and on the line x₁ - x₂ = 1. See the figure. The point (x₁,x2) that lies on the line x₁ + 3x₂ = 13 and on the line x₁ - x₂ = 1 is (Simplify your answer. Type an ordered pair.) X2 X₁ O

Find the point (x₁,x2) that lies on the line x₁ + 3x2 = 13 and on the line x₁ - x₂ = 1. See the figure. The point (x₁,x2) that lies on the line x₁ + 3x₂ = 13 and on the line x₁ - x₂ = 1 is (Simplify your answer. Type an ordered pair.) X2 X₁ O

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Finding the Intersection Point of Two Lines #### Problem Statement: Find the point \( (x_1, x_2) \) that lies on the line \( x_1 + 3x_2 = 13 \) and on the line \( x_1 - x_2 = 1 \). See the figure for the graphical representation. #### Graphical Representation: A graph showing two lines intersecting is displayed next to the problem statement. The x-axis (horizontal) is labeled as \( x_1 \) and the y-axis (vertical) is labeled as \( x_2 \). The lines intersect at a single point, indicating the solution to the given system of equations. #### Solution: To find the point \( (x_1, x_2) \) that satisfies both equations, we solve the system of linear equations given: 1. \( x_1 + 3x_2 = 13 \) 2. \( x_1 - x_2 = 1 \) Let's solve the system step-by-step. 1. Solve equation 2 for \( x_1 \): \( x_1 = x_2 + 1 \) 2. Substitute \( x_1 \) from equation 2 into equation 1: \( (x_2 + 1) + 3x_2 = 13 \) \( x_2 + 1 + 3x_2 = 13 \) Combine like terms: \( 4x_2 + 1 = 13 \) Subtract 1 from both sides: \( 4x_2 = 12 \) Divide by 4: \( x_2 = 3 \) 3. Substitute \( x_2 = 3 \) back into \( x_1 = x_2 + 1 \): \( x_1 = 3 + 1 = 4 \) Thus, the point \( (x_1, x_2) = (4, 3) \) lies on both lines. #### Answer: The point \( (x_1, x_2) \) that lies on the line \( x_1 + 3x_2 = 13 \) and on the line \( x_1 - x_2 = 1 \) is \( (4, 3) \). (Simplify your
Transcribed Image Text:### Finding the Intersection Point of Two Lines #### Problem Statement: Find the point \( (x_1, x_2) \) that lies on the line \( x_1 + 3x_2 = 13 \) and on the line \( x_1 - x_2 = 1 \). See the figure for the graphical representation. #### Graphical Representation: A graph showing two lines intersecting is displayed next to the problem statement. The x-axis (horizontal) is labeled as \( x_1 \) and the y-axis (vertical) is labeled as \( x_2 \). The lines intersect at a single point, indicating the solution to the given system of equations. #### Solution: To find the point \( (x_1, x_2) \) that satisfies both equations, we solve the system of linear equations given: 1. \( x_1 + 3x_2 = 13 \) 2. \( x_1 - x_2 = 1 \) Let's solve the system step-by-step. 1. Solve equation 2 for \( x_1 \): \( x_1 = x_2 + 1 \) 2. Substitute \( x_1 \) from equation 2 into equation 1: \( (x_2 + 1) + 3x_2 = 13 \) \( x_2 + 1 + 3x_2 = 13 \) Combine like terms: \( 4x_2 + 1 = 13 \) Subtract 1 from both sides: \( 4x_2 = 12 \) Divide by 4: \( x_2 = 3 \) 3. Substitute \( x_2 = 3 \) back into \( x_1 = x_2 + 1 \): \( x_1 = 3 + 1 = 4 \) Thus, the point \( (x_1, x_2) = (4, 3) \) lies on both lines. #### Answer: The point \( (x_1, x_2) \) that lies on the line \( x_1 + 3x_2 = 13 \) and on the line \( x_1 - x_2 = 1 \) is \( (4, 3) \). (Simplify your
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