Question

Solve this system of equations
-2x+5y+4z=-4
-5x-y+z=-1
2y+2z=-4

Answer 1

x = -1, y = 2 and z = -4.

Explanation:

-2x + 5y + 4z = -4 ......(A)

-5x - y + z = -1 .............(B)

2y + 2z = -4..................(C) Multiply (A) by 5 and (B) by -2:

-10x + 25y + 20z = -20 ....(D)

10x + 2y - 2z = 2 ..............(E) Adding D + E:

27y + 18z = -18 Dividing by 9:

3y + 2z = -2 ............(F) Subtract: (C) - (F):

-y = -2

y = 2.

Substitute for y is (C):

4 + 2z = -4

2z = -8

z = -4.

Substitute for y and z in (A):

-2x + 5(2) + 4(-4) = -4

-2x = -10 + 16 - 4 = 2

x = -1.