Question

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

Answer 1

Answer:

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.