How do you solve the system 3x - 4y - 2z = 13, 2x + y + 2z = 5, 6x +2y - z = 16?

1 Answer
Jan 26, 2018

Answer:

#color(blue)(x = 3, y = -1, z = 0)#

Explanation:

#3x - 4y - 2z = 13# Eqn (1)

#2x + y + 2z = 5# Eqn (2)

#6x + 2y - z = 16# Eqn (3)

Add Eqn (1), (2) to eliminate z

#5x - 3y = 18# Eqn (4)

Multiply Eqn (3) by 2 and add to Eqn (2)

#14x + 5y = 37# Eqn (5)

Find x & y by solving equations (4) & (5)

Multiply Eqn (4) by 5

#25x - 15y = 90# Eqn (6)

Multiply Eqn (5) by 3

#42x + 15y = 111# Eqn (7)

Adding Eqns (6) & (7)

#67x = 201# or #x = color(purple)(3)#

Substituting value of x in Eqn (4)

#(5 * 3) - 3y = 18#

#3y = 15 - 18 = -3#, #y = color(purple)( - 1)#

Substituting values of x & y in Eqn (3)

#(6*3) + (2 * (-1)) - z = 16#

#z = 18 - 2 - 16 = 0#

#z = color (purple)(0)#

#color(blue)(x = 3, y = -1, z = -0)#