solve the following system of equations with your choice of number in the box.

Question

3x+2y=7
-3x-2y= (box)

Answer 1

The given system of equations is:

3x + 2y = 7 ............(1)
-3x - 2y = (box) ............(2)

To solve this system, we'll use the method of elimination.

Adding equation (1) and equation (2), the x-terms and y-terms cancel out:

(3x + 2y) + (-3x - 2y) = 7 + (box)
(3x - 3x) + (2y - 2y) = 7 + (box)
0 + 0 = 7 + (box)
0 = 7 + (box)

No matter what number we choose for the box, the equation 0 = 7 + (box) will never hold true.

Therefore, there is no number that we can put in the box to solve the system of equations. The system is inconsistent, meaning there is no solution.