Question

Solve the system below

Answer 1

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.