Answer: x=-1, y=8 and z=-5.
Step-by-step explanation:
The given system of equations:
3x - 5y + 2z = -53 (i)
x - 7y - 4z = -37 (ii)
5x + 9y + 2z = 57 (iii)
Multiply 3 to equation (ii)
3x-21y-12z= -111 (iv)
Eliminate (iv) from (i) , we get
-5y+21y+2z+12z=-53+111
⇒ 16y+14z=58
⇒ 8y+7z=29 (v) [divide equation by 2]
Multiply 5 to equation (ii)
5x-35y-20z= -185 (vi)
Eliminate (vi) from (iii) , we get
9y+35y+2z+20z=57+185
⇒ 44y+22z=242
⇒ 2y+z=11 [divide equation by 22]
⇒ z= 11-2y (vii)
Put value of z in (v) , we get
8y+7(11-2y)=29
⇒ 8y+77-14y=29
⇒ 6y=48
⇒ y=8
Put value of y in (vii), we get z= 11-2(8) =11-16=-5
i.e. z=-5
Put y=8 and z=-5 in (ii) , we get
x - 7(8) - 4(-5) = -37
⇒x-56+20=-37
⇒ x-36=-37
⇒ x = -37+36
⇒ x = -1
Hence, x=-1, y=8 and z=-5.
