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1. (3, -2) is a solution to the system of equations x – 2y = 7 and 2x + 3y = 0, (3, -2) is not a solution to the system of equations  -x – y = -5 and 3x – 4y = 17 and (3, -2) is not a solution to the system of equations x + y = 1 and x – y = 6

   How to determine the whether or not (3, -2) is a solution to the following systems?

   The systems of equations are given as:

   1. x – 2y = 7 and 2x + 3y = 0

   2. -x – y = -5 and 3x – 4y = 17

   3. x + y = 1 and x – y = 6

   Next, we substitute (3, -2) for (x, y) in the system of equations.

   So, we have:

   1. x – 2y = 7 and 2x + 3y = 0

   3 – 2 * -2 = 7 and 2 * 3 + 3 * -2 = 0

   Evaluate

   7 = 7 and 0 = 0

   The above equation is true

   Hence, (3, -2) is a solution to the system of equations x – 2y = 7 and 2x + 3y = 0

   2.- x – y = -5 and 3x – 4y = 17

   -3 + 2 = -5 and 3 * 3 + 4 * 2 = 17

   Evaluate

   – 1 = – 5 and 1 7 = 1 7

   The above equation is false

   Hence, (3, -2) is not a solution to the system of equations  -x – y = -5 and 3x – 4y = 17

   3. x + y = 1 and x – y = 6

   3 – 2 = 1 and 3 + 2 = 6

   Evaluate

   1 = 1 and 5 = 6

   The above equation is false

   Hence, (3, -2) is not a solution to the system of equations x + y = 1 and x – y = 6

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