Problem 98 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.

Step 3: 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.