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Chapter 5: Problem 98

Write a system of equations having \(\\{(-2,7)\\}\) as a solution set. (More than one system is possible.)

Short Answer

Expert verified
The system of equations that has (-2,7) as its solution could be \(y = x + 9\) and \(2y = 3x + 20\).

Step by step solution

01

Formulate the first equation

Lets identify the pair (-2,7) as coordinates (x,y). One possible equation can be determined by formulating a simple linear relationship where x and y appear one time each. For instance, an equation can be \(y = x + 9\). Substitute (-2,7) into this equation would yield: 7 = -2 + 9, which holds true.
02

Formulate the second equation

Creating a second equation with a slightly more complicated relationship between x and y could produce a system of equations. For example, take the equation \(2y = 3x + 20\). Substitute (-2,7) into this equation: 2*7 = 3*(-2) + 20, we obtain 14 = -6 + 20, which is also true.
03

Write down the system of equations

Combine the two equations to form a new system of equations: \(y = x + 9\) and \(2y = 3x + 20\). Verify that for x = -2, y = 7 indeed holds true for both equations.

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