1) {x,y,z}={4,-5,3}
2) 200 km
Hi, i was just wondering if anyone could help me out with these two math questions from my homework.
question 1.) solve the system of equations
x+3y-z=-14
7x+6y+z=1
4x-2y-5z=11
question 2.)a tain leaves toronto for montreal at the same time as another train leaves montreal for toronto. the cities are 500km apart. The trains pass each other 2 hours later. the train leaving montreal is travelling 50km/h faster than the one leaving from toronto. at what distance away from toronto do the trains pass each other?
1.) One method we may use is elimination. I would begin by taking the first two equations:
Notice if we add the equations together, we will eliminate the z:
Next, we could take -5 times the first equation and add it to the third to also eliminate z: Then you will have a 2X2 system in x and y, which you may solve, then you will be able to find z from any of you original equations.
2.) Let train 1 be the train that departed Toronto, and train 2 be the train that departed Montreal. We will subscript all variables accordingly. We are being asked to find
After traveling for 2 hours, the trains meet, so we know the sum of their traveled distances is 500 km:
We are also told:
The relationship between distance, speed and time is , so we may state:
Using the above information, you can find the quantity in question.
Hello, njdevils1833!
Another approach . . .
2) A train leaves Toronto for Montreal at the same time as another train leaves Montreal for Toronto.
The cities are 500km apart. .The trains pass each other 2 hours later.
The train leaving Montreal is travelling 50km/hr faster than the one leaving from Toronto.
At what distance away from Toronto do the trains pass each other?
Let = speed of the train leaving Toronto.
Then = speed of the train leaving Montreal.
In 2 hours, they meet atCode:: 2v : 2(v+50) : *-------->*<--------------* T X M : - - - - - 500 - - - - - :
The train from Toronto has traveled km.
The train from Montreal has traveled km.
Together, they covered 500 km: .
. . Hence: . km/hr.
Therefore, is: km from Toronto.