Can someone help me with this question?
What is the solution to the system of equations?
{3x+2y+z=9
-3x-y+3z=-7
2x +z=9

A.(4, 2, 1)
B.(-4, -2, 1)
C.(4, -2, 1)
D.(4, -2, -1)

Question

Can someone help me with this question?
What is the solution to the system of equations?
{3x+2y+z=9
-3x-y+3z=-7
2x         +z=9

A.(4, 2, 1)
B.(-4, -2, 1)
C.(4, -2, 1)
D.(4, -2, -1)

mathmate · Answer

Most of the time, with solutions of 3x3 systems, it is faster to test each solution by substituting values into each of the three equations.

If you want to avoid testing all three equations 4 times, you can also test a single equation (formed by the sum of all three), and see how many of the four satisfy.

If only one solution satisfies, that is the one.  If more than one does, then they have to be checked individually.
For this case, the sum would be 
2x+y+5z=11
and only one of the solutions satisfies this equation.