Determine whether the ordered triples listed are solutions of the system of linear equations.

Question

x+y+2z=12

5x+y+z= -9

-5x+2y+3z=47

(a) (-3,3,6) (b) (-4,6,5)

Answer 1

Just plug in the values into the equations. I'll start you off with (-3, 3, 6). That's x = -3, y = 3, z = 6:

x + y + 2z = 12

-3 + 3 + 2(6) = 12

0 + 12 = 12

12 = 12

So it works for this equation. . If you end up with nonsense, such as 3 = -7, then the ordered triple is NOT a solution. Try (-3,3,6) on the other two equations. It has to work for all three equations for the ordered triple to be a solution; that is, you have to end up with -9 = -9 and 47 = 47:

5x+y+z= -9

-5x+2y+3z=47

Then repeat the process for the other ordered triple.