Show that x=10, y = 4, and z = 7 is a solution to the system below without solving the system formally x+2y+z=25 4x-y-5z=1 -2x-y+82=32

Answer 1

Solution: Just plug the x-, y-, and z-values you have into x, y, and z into each equation and check that you get three true statements out of it. If this is the case, your point is a solution of the system. If even one resulting statement is false, the point is not a solution of the system.

x + 2y + z = 25

4x - y - 5z = 1

-2x - y + 82 = 32

Proposed solution: (10, 4, 7)

(10) + 2(4) + (7) = 25

4(10) - (4) - 5(7) = 1

-2(10) - (4) + 82 = 32

Evaluate and make sure these statements are true. If even one is false, you don't have the solution in the point (10, 4, 7). I hope this helps!