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Chapter 2: Problem 2

The lines graphed in the \(x y\)-plane above represent a system of two linear equations. What is the solution \((x, y)\) to the system? A) \((-1,-6)\) B) \((0,-3)\) C) \((2,3)\) D) \((3,0)\)

Short Answer

Expert verified
After analyzing the given options and testing each one to see if it satisfies both linear equations, we find that the solution to the system is option C, \((2,3)\).

Step by step solution

01

Analyze the given options

We have been given four different options, and we need to find the one that satisfies both linear equations. Let's check each option one by one.
02

Test option A

Let's test option A, which is \((-1,-6)\). If this point lies on both lines, it would be the solution to the system. Substitute the \(x\) and \(y\) values into the equations of both lines and see if they hold true. If not, move to the next option.
03

Test option B

Now, let's test option B, which is \((0,-3)\). If this point lies on both lines, it would be the solution to the system. Substitute the \(x\) and \(y\) values into the equations of both lines and see if they hold true. If not, move to the next option.
04

Test option C

Now, let's test option C, which is \((2,3)\). If this point lies on both lines, it would be the solution to the system. Substitute the \(x\) and \(y\) values into the equations of both lines and see if they hold true. If this satisfies both equations, we have found the solution.
05

Test option D (if necessary)

If none of the previous options are the solution, we will test option D, which is \((3,0)\). If this point lies on both lines, it would be the solution to the system. Substitute the \(x\) and \(y\) values into the equations of both lines and see if they hold true. If this satisfies both equations, we have found the solution. After testing all of the given options, we will find the one that satisfies both linear equations and represents the solution to the system.

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