Q:

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)

Accepted Solution

A:
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) = 82y =  8 + 16 - 10 = 14y = 7.