If 3x + 2y + 5z = 10 and....

[Ineedhelp]

If 3x + 2y + 5z = 10 and 6x + 4y = 12, what is the value of z?


Can you please explain the process of solving. Please be thorough.


Thanks.

[tim]

Before we help with this question, we'd like you to show some effort of your own. What did you try on this question? Where did you get stuck?

[Ineedhelp]

My effort is all wrong on this. By the time I reached this problem, I completely panicked on time, and the fact that there was 3 variables, and I needed to solve for one. I made the mistake of combining like terms, which gave me 9x+6y+5z=22, I knew I was wrong, because I thought about it. The answer was not natural for me to solve. I guessed and moved on.

[RonPurewal]

If 3x + 2y + 5z = 10 and 6x + 4y = 12, what is the value of z?


Can you please explain the process of solving. Please be thorough.


Thanks.

this post violates the forum rules, which specify that you must post all questions in their entirety, including all answer choices. i'll answer this one, but then we'll respond to all other questions posted in the same way with "sorry, please post the entire question as requested".

here's the short version:

* you want "z". this means that you want to get rid of "x" and "y".
(this is the most important part of any math problem: HAVING A GOAL that you actually set out to achieve. if you are just pushing numbers and variables around at random, then you aren't going to get very far with most problems.)

* notice that the left-hand part contains "3x + 2y".

* notice that the right-hand part contains "6x + 4y", which is exactly twice "3x + 2y".

* so, cut both sides of the right-hand equation in half.

* subtract it from the left-hand equation; this will kill "x" and "y".

boom! you can find z.