Need to set up a system of equations then an augmented matrix of that system and use elementary row operations on the augmented matrix to replace the system with an equivalent system that is easier to solve **Topic: Solving Systems of Linear Equations Graphically****Find the Point of Intersection for Two Linear Equations**In this exercise, we aim to find the point \((x_1, x_2)\) that lies on the intersection of two lines. The equations for these lines are:1. \(x_1 + 2x_2 = 6\)2. \(x_1 - x_2 = 3\)Refer to the accompanying graph for a visual representation.**Graph Explanation**The graph provided depicts two lines on a coordinate plane. The axes are labeled as \(x_1\) (horizontal axis) and \(x_2\) (vertical axis). The lines are colored blue.- The first line (\(x_1 + 2x_2 = 6\)) slopes downward from left to right.- The second line (\(x_1 - x_2 = 3\)) slopes upward from left to right.The point where the two lines intersect represents the solution \((x_1, x_2)\) to the system of equations. This is the point common to both lines.**Conclusion**The point \((x_1, x_2)\) that satisfies both equations simultaneously is the point of intersection on the graph. Analyze the graph to determine the coordinates of this point and verify it satisfies both equations.

Answered: Image /qna-images/answer/364814bc-51e2-4ff1-a4f5-f2bbee5d3283.jpg

Answered: X2 Find the point (x1,x2) that lies on…

X2 Find the point (x1,x2) that lies on the line x, + 2x2 = 6 and on the line x, - x2 = 3. See the figure. The point (x4,X2) that lies on the line x, + 2x2 = 6 and on the line x, - X2 = 3 is

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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Question

Need to set up a system of equations then an augmented matrix of that system and use elementary row operations on the augmented matrix to replace the system with an equivalent system that is easier to solve

**Topic: Solving Systems of Linear Equations Graphically**

**Find the Point of Intersection for Two Linear Equations**

In this exercise, we aim to find the point \((x_1, x_2)\) that lies on the intersection of two lines. The equations for these lines are:

1. \(x_1 + 2x_2 = 6\)
2. \(x_1 - x_2 = 3\)

Refer to the accompanying graph for a visual representation.

**Graph Explanation**

The graph provided depicts two lines on a coordinate plane. The axes are labeled as \(x_1\) (horizontal axis) and \(x_2\) (vertical axis). The lines are colored blue.

- The first line (\(x_1 + 2x_2 = 6\)) slopes downward from left to right.
- The second line (\(x_1 - x_2 = 3\)) slopes upward from left to right.

The point where the two lines intersect represents the solution \((x_1, x_2)\) to the system of equations. This is the point common to both lines.

**Conclusion**

The point \((x_1, x_2)\) that satisfies both equations simultaneously is the point of intersection on the graph. Analyze the graph to determine the coordinates of this point and verify it satisfies both equations.

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