CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Solve the following system of linear equation in three variables.
5x + 6y + 8z = 0
3x + 4y + 6z = 0
3x + 5y + 16z = 7

A
x=2 , y= 4 and z=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
x=2 , y= -3 and z=2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x=2 , y= -3 and z=1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
x=3 , y= -3 and z=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C x=2 , y= -3 and z=1
We have,
5x + 6y + 8z = 0.............(1)
3x + 4y + 6z = 0..............(2)
3x + 5y + 16z = 7.............(3)

Multiplying equation (1) by 3 and equation (2) by 5, we get

15x+18y+24z=0 ................(4)
15x+20y +30z =0 ..............(5)

Subtracting equation (5) from equation (4) , we get

-2y-6z =0

y+3z =0 ............(6)

Subtracting equation (3) from equation (2) , we get

-y -10z = -7 ....................(7)

Adding equations (6) and (7), we get

-7z = -7
z= 1

Putting z=1 in the equation (6), we get

y + 3(1) =0

y= -3

Putting z=1 and y= -3 in the equation (1), we get

5x+ 6(-3) +8(1) =0

5x -18 +8 =0

5x=10

x=2

Thus, we have x=2 , y= -3 and z=1

Check/Verification :

Substituting the values of x,y and z in the equation (3), we get

LHS = 3(2) +5 (-3) +16 (1)
= 6-15+16
= 7
=RHS

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adaptive Q37
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon