Solve the system?

Question

(x-2y+z=-1 over
(-2x+3y+2z=4 over
(2x+y+3z+9

possible answers are the following:
a. (-6, -2, 1)
b. (-5, -2, 0)
c. (2,2,1)
d. (9,6,2)

Answer 1

Why don't you tell us what level you are at, and what area you are studying, then perhaps we could give an answer tht is more helpful..this can be done with matrices, or a 3 d grapher, Using Cramer's method of determinants and more, but if you are restricted to doing linear combinations of the three equations, those would not be of much use to you...

also the last item has no equal sign??? I assume =9 is correct...

I just did the whole mess on a calculator using Reduced Row echelon matrices and it gave 4/3, 22/21, 37/21 for the x,y,z solution...

Answer 2

a million. resolve for between the variables. that is least complicated to apply the 2d equation. So interior the 2d equation upload y to the two aspects and additionally you get x=4+y 2. Then, replace that for the period of for the x in equation1 to get 3(4+y)+2y=12 3. Distribute the three to get 12+3y+2y=12 4. Subtract 12 from the two aspects to get 3y+2y=0.5. upload y's jointly to get 5y=0 6. Divide via 5 and y=0 7. Plug y=0 into the 2d equation and additionally you get x=4 So, you have been suitable! x=4 and y=0

Answer 3

-2x + 3y + 2z = 4
2x + y + 3z = 9--------ADD
4y + 5z = 13

2x - 4y + 2z = - 2
-2x + 3y + 2z = 4----ADD
- y + 4z = 2----X by 4

-4y + 16z = 8
4y + 5z = 13---ADD
21z = 21
z = 1

4y + 5 = 13
4y = 8
y = 2

x - 4 + 1 = - 1
x = 2
Solution (2,2,1) is OPTION c.