Finding value of expression

[Yuvraj Singh]

The expression for which we have to find the value consists of three variables. The other 2 equations consist of 3 variables. How to find the value of expression then?

 

[tkhunny]

Hint:

7x + 5y + 11z = 44
33x + 2y + 5z = 23
---------------------
40x + 7y + 16z = 67

 

[Dr.Peterson]

View attachment 13182

The expression for which we have to find the value consists of three variables. The other 2 equations consist of 3 variables. How to find the value of expression then?

When it looks like there's too little information, you can guess that maybe the problem is designed specially to have a solution anyway, so just proceed with solving, and hope for the best. Trust the author of the problem.

You won't be able to fully solve for all three variables, but you can express, say, y and z in terms of x. Plug those into the given expression, and maybe x will cancel out, and the result will be a constant. Or there may be a quicker way, as tkhunny hinted that you might be able to find just the right combination of the two equations. I wouldn't spend much time looking for that, though.

Now, in real life you don't expect equations to be fine-tuned like this; but sometimes this happens even there!

 

[piyush]

Hint:

7x + 5y + 11z = 44
33x + 2y + 5z = 23
---------------------
40x + 7y + 16z = 67

How to proceed further?

 

[tkhunny]

7(7x + 5y + 11z) = 7(44)
-15(33x + 2y + 5z) = -15(23)
-------------------------
-446x + 5y + 2z = -37

You will have to explore what factors will help you toward your goal.

1, 1 didn't do it in the first hint.
7, -15 didn't do it in this example.
How can you get it to do it?