Hi, could someone help me understand the why answer to this question is 5:

3x+2y+2z=19 and 3x+y+z=14 - if the equations on the left are true, which of the following is the value of y+z? Answer: 5

Question

Hi, could someone help me understand the why answer to this question is 5:      

3x+2y+2z=19   and  3x+y+z=14      - if the equations on the left are true, which of the following is the value of y+z?    Answer:   5

aroub · Answer

3x+2y+2z=19... (1)
3x+y+z=14...(2)

Maybe the best thing to do here is to solve it by linear combination.

Eq1+ Eq2 (-1) 

=> 

3x+2y+2z=19
-3x-y-z=14
-------------
y+z=5

aroub · Answer

Sorry -14

anonymous · Answer

You can add or subtract any number to both sides of an equation and the equation still holds. If left hand side equals right hand side of the second equation, then you can treat each side as being the same number. Therefore, subtract left hand side of equation two from equation one, and subtract right hand side of equation two from right hand side of equation one. This is the same as subtract one number from each side of equation one, so the equation still holds.. See what you end up with.