CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

In the system of equation 1x+1y+1z=6,2x3y+4z=8 and 3x4y+5z=10, values of x, y and z which satisfy the above three equations, will be

A
12, 1 and 13
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
13, 1 and 12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1,12 and 13
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
1,13 and 12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 1,12 and 13
If 1x=A,1y=B and 1z=C, then the given equation will be written as:
A+B+C=6.........(i)
2A3B+4C=8 ...............(ii)
3A4B+5C=10 ..... (iii)
On multiplying equation (i) by 3 and adding it to equation (ii),
(3A+3B+3C)+(2A3B+4C)=6×3×8
5A+7C=26 ...... (iv)
On multiplying equation (i) by 4 and adding it to equation (iii),
(4A+4B+4C)+(3A4B+5C)=6×4+10
7A+9C=34 ..... (v)
On multiplying equation (iv) by 7 and equation(v) by 5 and subtracting equation (v) from equation (iv),
(35A+49C)(35A+45C)=26×734×5
4C=182170=12C=124=3
On substituting this value of C in equation (iv),
5a+7×3=265A=26215A=5
A=55=1
From equation (i), 1+B+3=6B=64=2
1x=A=1x=1,1y=B=2y=12
and 1z=C=3z=13
Hence values of x, y and z will be 1,12 and 13 respectively.

flag
Suggest Corrections
thumbs-up
0
mid-banner-image
mid-banner-image
similar_icon
Related Videos
thumbnail
lock
Algebraic Solution
MATHEMATICS
Watch in App