In the given question, two equations numbered l, II, and III are given. Solve all the equations and mark the appropriate answer.
I. 3x + 7y + 11z = 54
II. 4x + 9y + 13z = 61
III. 5x + 3y + 7z = 28I. 3x + 7y + 11z = 54 (i)
II. 4x + 9y + 13z = 61 (ii)
Now multiply equation (i) by 4 and multiply equation (ii) by 3
⇒ 12x + 28y + 44z = 216 (iii)
⇒ 12x + 27y + 39z = 183 (iv)
Now subtract equation (iv) from (iii), and we get
⇒ y + 5z = 33 (v)
Now by
II. 4x + 9y + 13z = 61 (vi)
III. 5x + 3y + 7z = 28 (vii)
Now multiply equation (vi) by 5 and multiply equation (vii) by 4
⇒ 20x + 45y + 65z = 305 (viii)
⇒ 20x + 12y + 28z = 112 (ix)
Now subtract equation (ix) from (viii), and we get
⇒ 33y + 37z = 193 (x)
Now multiply equation (v) by 33 and subtract from equation (x)
⇒ (33y + 37z) – (33y + 165z) = 193 – 1089
⇒ 128z = 896
⇒ z = 7
Now put the value of z in equation (v)
⇒ y + 5 × 7 = 33
⇒ y = 33 – 35 = 2
Now put the value of y and z in equation (i)
⇒ 3x + 7 × (2) + 11 × 7 = 54
⇒ 3x – 14 + 77 = 54
⇒ 3x = 54 – 63
⇒ x = 9/3 = 3
Value of x 
Value of y 
Value of z 
Relation 
3 
2 

x < y 
3 

7 
x < z 

2 
7 
y < z 
3 
2 
7 
x < y < z 