Solve the system of equations. 4x+2y+5z=8 5x+3y+4z=9 6x+3y+3z=3

A) (x=-3, y=6, z=1)

B) (x=-5, y=8, z=3)

x = - 4, y = 7, z = 2.

Step-by-step explanation:

4x + 2y + 5z = 8 ... (1)

5x + 3y + 4z = 9 ... (2)

6x + 3y + 3z = 3 ... (3)

Subtract: equation (2) - equation (3):

-x + z = 6 ... (4)

Multiply (1) by 3 and (2) by 2:

12x + 6y + 15z = 24 ... (5)

10x + 6y + 8z = 18 ... (6)

Subtract: (5) - (6):

2x + 7z = 6 ... (7)

Multiply equation (4) by 2:

- 2x + 2z = 12 ... (8)

Add (7) + (8):

9z = 18, so z = 2.

Substitute for z in equation (4)

-x + 2 = 6

-x = 4 so x = - 4.

Now find y by substituting in equation (1):

4 (-4) + 2y + 5 (2) = 8

2y = 8 + 16 - 10 = 14

y = 7.