Ok, so I completely forget all of these, lol, it's sad, just did them a few years ago. 1. Solve the following systme of linear equations. 4x + 3y = 13 5x + y - 8 = 0 2.An apartment building has 80 units. 1 bedroom for $850, 2 bedroom for $1050. The monthly income is 78 400$. How many of each type are there? 3.explain the steps to use the elimination method for the following: 5x + 2y = 5 3x - 4y = -23 4. three bricklayers and 4 carpenters earn $910 per day. 10 bricklayers and 5 carpenters earn 1850$ a day a) set up a system of equations b) is there an advantage to eliminating either variable first? c) determine the daily wage of the bricklayer 5. tickets are sold for 7$ in advance and $9.50 at the door. 300 tickets were sold for a total of $2405.00. How many of each were sold? Thanks, if somebody could help explain the steps for these, it would help.
o1. x = 1 y = 3 Code (Text): 4x + 3y = 13 5x + y - 8 = 0 get rid of the y variable by multiplying the second equation by -3 4x + 3y = 13 -15x + -3y + 24 = 0 add the two equations together -11x + 24 = 13 move the 24 to the right side -11x = -11 solve x = 1 substitute x into the first equations 4(1) + 3y = 13 3y = 9 y=3 o2. 1 bedroom = 28 2 bedroom = 52 Code (Text): x = 1 bedroom y = 2 bedroom two equations x + y = 80 850x + 1050y = 78400 solve the first equation for y y = 80 - x substitute into the second equation 850x + 1050(80 - x) = 78400 simplify -200x + 84000 = 78400 solve -200x = -5600 x = 28 substitute into the first equation x + y = 80 28 + y = 80 y = 52 o3. Code (Text): multiply the first equation by 2 10x + 4y = 10 3x - 4y = -23 add the two equations together 13x = -13 solve x = -1 substitute x into first equation 10(-1) + 4y = 10 4y -10 = 10 4y = 20 y = 5 o4. Code (Text): x = bricklayer y = carpenter a) set up a system of equations 3x + 4y = 910 10x + 5y = 1850 b) is there an advantage to eliminating either variable first? not that I see...but since question c asks to find the wage of a bricklayer, I'd eliminate y first so I don't have to solve for both x and y... c) determine the daily wage of the bricklayer multiply the first equation by -5 and the second by 4 -15x - 20y = -4550 40x + 20y = 7400 add the two equations together 25x = 2850 solve x = 114 o5. tickets sold in advance = 178 tickets sold at the door = 122 Code (Text): x = ticket sold in advance y = ticket sold at the door two equations x + y = 300 7x + 9.5y = 2405 solve the first equation for y y = 300 - x substitute into the second equation 7x + 9.5(300 - x) = 2405 simplify -2.5x + 2850 = 2405 solve -2.5x = -445 x = 178 substitute x into the first equation 178 + y = 300 y = 122 NOTE : tac123 finished problems 2-5 before me so all credit goes to him/her...
1. Solve the following systme of linear equations. 4x + 3y = 13 5x + y - 8 = 0 5x + y = 8 x 3 15x + 3y = 24 4x+3y=13 take em away from each other 11x = 11. X = 1. Then put 1 into the equation. 4x + 3y = 13, 4x = 4 + ?? = 13, Therfore 3y = 9 so y = 3. x = 1 || y = 3 (ill look at others later ) Damn you lazypando
| 5 1 8 | | 4 3 13 | 1 -2 -5 4 3 13 1 -2 -5 0 11 33 1 -2 -5 0 1 3 1 0 1 0 1 3 x = 1 y = 3 -------- x + y = 80 850*x + 1050*y = 78400 1 1 80 850 1050 78400 1 1 80 0 200 10400 1 1 80 0 1 52 1 0 28 0 1 52 28 single bedroom, 52 doubles ------ 5x + 2y = 5 3x - 4y = -23 multiply first equation by 2 10x + 4y = 10 3x - 4y = -23 add both equations 13x + 0y = -13 so x = -1 substitute x into equation for y 3(-1) - 4y = -23 solve for y y = -20 / -4 = 5 ----- 3 b + 4 c = 910 10 b + 5 c = 1850 b) trivial no matter which variable is eliminated first c) 3 4 910 10 5 1850 3 4 910 2 1 370 1 3 540 2 1 370 1 3 540 0 -5 -710 1 3 540 0 1 142 1 0 114 0 1 142 brick layer has a wage of $114 --- a + d = 300 7 a + 9.5 d = 2405 1 1 300 7 9.5 2405 1 1 300 0 2.5 305 1 1 300 0 1 122 1 0 178 0 1 122 advanced sales 178 tickets door sales 122 tickets Same steps as the problems above
I just don't think it is very fair, because i'm sure I started my problems before lazy panda, and I also finished before her. Except she posted when she only had 1 problem done, and then edited as she worked, so now she looks like she was faster than me :-(. If you look at the times she finished her first problem at 12:38, and i finished my last problem at 12:41. Oh well, now i know the posting strategy for next time. :twisted:
Quit whining. It's not like it was a competition The fact that you both got the same answers is a good thing regardless of who did it first.
No they were done, but there were 2 things. On the first problem, I made one of the numbers 1 instead of a 3, so I figured I would change that for him so that it was exactly his problem instead of just an example problem. Also, on another problem I just wrote down the wrong final solution, so I edited that. The other two were just formatting changes. But my work was there. *exasperated* Fine, I think we should have an independent party setup a math contest, and then we can go head to head.
Aww... you're too nice. You probably helped him more though, your answers are nicely formated and explained, I just used Gaussian elimination and you can't really display it as well when you write it online as when you do it by hand.
there is a solution to that ... it takes a bit more time but turns out nicely formated...just download MathEQ Expression Editor and upload the images...
if you study hard on algebra's or college math.. im sure you will love it. and im get ready on that..next 2 weeks is my 1st college life.[/code]
Wow, looks like there are some Mathematics experts here. If I have Differentiation and Integration problems I know who to look for now.