Struggling with "Forming simultaneous equations in three unk

[Guest]

I've been struggling with maths this whole year as my maths teacher, tries to make us bruteforce assessments, by telling us what to do instead of teaching us. He's started "teaching" us this sort of question, and it's just going straight over my head. http://imgur.com/a/cbFGT these are some of the examples of what we're learning, and the sites we've been told to use solving the questions ncalculators.com/algebra/3-variable-equation-solver.htm and http://www.wolframalpha.com/widgets/vie ... cc07b0d5eb. I'm failing at school this year and despritely need a tutor, or help, or anything. Just anything anyone can give. Please...

[HallsofIvy]

No "tutors" here but we will help you if you show us what you do know and what you can already do by showing us your attempts to solve problems. Have you not tried anything yourself?

I also am not clear what it is you want. You titled this "Forming simultaneous equations in three unk" but the first page you post is has equations already given. All those problems are linear but the WolframAlpha page you link to has a non-linear equatio.

It is the second page that is titled "forming simultaneous equations". Is that what you are asking about? there are a lot of exercises on that page but #6 is underlined so I will look at it:

6. One week Thomas received 24 pieces of mail. The number of bills was two less than twice the number of letters. The number of pieces of junk mail was 2 more than 5 times the number of letters. How many letters, bill, and pieces of junk mail did Thomas receive that week?

Okay, there are three things we want to determine, the number of letters, the number of bills, and the number of pieces of junk mail so let L= number of letters, B= number or bills, and J= number of pieces of junk mail. Because there are three unknowns, we need three equations and there are three statements about these quantities. As usual each statement gives an equation!

"One week Thomas received 24 pieces of mail." So L+ B+ J= 24.

"The number of bills was two less than twice the number of letters." B= 2L- 2.

"The number of pieces of junk mail was 2 more than 5 times the number of letters," J= 5L+ 2.

So we want to solve the three equations, L+ B+ J+ 24, B= 2L- 2, and J= 5L+ 2. Since the last two equations give B and J in terms of L we can replace B and J in the first equation with that: l+ 2L- 2+ 5L+ 2= 8L= 24. L=24/8= 3. B= 2L- 2= 2(3)- 2= 6- 2= 4. J= 5L+ 2= 5(3)+ 2= 15+ 2= 17.

Thomas received 3 letters, 4 bills, and 17 pieces of junk mail. (Sounds a lot like my mail!)

Check:
L+ B+ J= 3+ 4+ 17= 24. Yes, Thomas received a total of 24 pieces of mail.
B= 2L- 2= 2(3)- 2= 6- 2= 4. Yes, the number of bills was 2 less than twice the number of letters.
J= 5L+ 2= 5(3)+ 2= 15+ 2= 17. Yes, the number of pieces of junk mail was 2 more than 5 times the number of letters.