Question 22

If $$2x + 3y - 5z = 18, 3x + 2y + z = 29$$ and $$x + y + 3z = 17$$, then what is the value of $$xy + yz + zx$$?

Solution

x+y+3z=17..........(1)

2x+3y-5z=18.......(2)

3x+2y+z=29........(3)

Now, (1)×2-(2) :

11z-y=6......(4)

And, (3)×2-(2)×3 :

17z-5y=4............(5)

Now,4×(4)-(5) :

z=2 .

Now, put this value in (4) ,we get :

y=6.

From equation (1) we get : x=5.

So,xy+yz+xz=10+30+12=52.

B is correct choice.

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