Question : If 3x + 4y – 2z + 9 = 17, 7x + 2y + 11z + 8 = 23, and 5x + 9y + 6z – 4 = 18, then what is the value of x + y + z – 34?
Option 1: –28
Option 2: –14
Option 3: –31
Option 4: –45
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Correct Answer: –31
Solution :
Given:
3x + 4y – 2z + 9 = 17 .......(i)
7x + 2y + 11z + 8 = 23 .......(ii)
5x + 9y + 6z – 4 = 18 ..........(iii)
By adding equation (i), (ii), and (iii), we get,
15x + 15y + 15z + 13 = 58
⇒ 15(x + y + z) = 45
⇒ (x + y + z) = 3
⇒ (x + y + z) – 34 = 3 – 34
$\therefore$ (x + y + z) – 34 = –31
Hence, the correct answer is –31.
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