If 2x + 3y – 5z = 18, 3x + 2y + z = 29 and x + y + 3z = 17, then what is the value of xy + yz + zx?
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Correct answer: B
Explanation
The correct answer is option 2 i.e. 52
2x + 3y - 5z = 18 .....(1)
3x + 2y + z = 29 .....(2)
x + y + 3z = 17 .....(3)
Adding equation (1), (2) and (3)
⇒ 6x + 6y - z = 64 .....(4)
Multiplying equation(3) by 6
⇒ 6x + 6y + 18z = 102 .....(5)
By subtracting (4) and (5)
⇒ -19z = -38
⇒ z = 2
Put the value of z in equation (1) and (3)
2x + 3y = 28 .....(6)
x + Y = 11 .....(7)
By solving equation (6) and (7)
⇒ x = 5, y = 6
Hence,
xy + yz + zx = 5 × 6 + 6 × 2 + 2 × 5 = 30 + 12 + 10
xy + yz + zx = 52