2x + 4y + z = 3

x - 2y - 3z = 4

x + y - z = - 1

A) 2x + 4y + z = 3

B) x - 2y - 3z = 4

C) x + y - z = - 1

Multiplying B & C by - 1

B) - x + 2y + 3z = - 4

C) - x - y + z = + 1 Then adding to A

A) 2x + 4y + z = 3

5y + 5z = 0

So basically z = - y

A) 2x + 4y - y = 3

B) x - 2y + 3y = 4

C) x + y + y = - 1

A) 2x + 3y = 3

Multiplyig B by - 2

B) - 2x - 2y = - 8

C) x + 2y = - 1 Adding B&C

-x = - 9

x = 9

A) 2*9 + 4y + z = 3

A) 4y + z = - 15

B) 9 - 2y - 3z = 4

B) - 2y - 3z = - 5

A) 4y + z = - 15

B) - 2y - 3z = - 5

Multiplying A by 3

A) 12y + 3z = - 45

B) - 2y - 3z = - 5 Then adding A & B

10y = - 50

y = - 5

C) x + y - z = - 1

C) 9 - 5 - z = - 1

C) 5 = z

So x = 9

y = - 5

z = 5

Wow!