4x−4y+4z=−4, 4x+y−2z=5, −3x−3y−4z=−16

Question

Solve by Substitution Method:

4x−4y+4z=−4 

4x+y−2z=5 

−3x−3y−4z=−16

Answer 1

Solve by Substitution Method:

4x − 4y + 4z = −4 ------------ (1)

4x + y −2z = 5      ------------ (2)

−3x − 3y − 4z = −16  -------- (3)

Substituting for y = -4x + 2z + 5, from (2), into (1) and (3) gives us

9x – 10z = -1   --------- (4)

5x – z = 4     ------------ (5)

Substituting for z = 5x – 4, from (5), into (4) gives us

9x – 50x + 40 = -1

-41x = -41

x = 1

z = 5x – 4 = 5 – 4

z = 1

y = -4x + 2z + 5 = -4 + 2 + 5

y = 3

Solution is: x = 1, y = 3, z = 1