How to write a system of equations from a word problem?
964853
Let X = number of rabits\nY = number of chickens\n\nX = Y + 6\n\nWe know chickens have two legs and rabbits have 4 legs, so the number of legs is\n\n4X + 2Y = 54\n\nOur system of equation is:\nX-Y = 6\n4x + 2Y = 54\n\nmultiple equation 1 by -4 and add to equation 2 to eliminate x\n6Y = 30\nY = 5\nX = 6 + Y = 11\n\nPlease check for errors\n\nPlease note that in the answer you gave above that 30 rabbits have 120 legs plus the 48 legs of the chickens well exceeds the 54 legs requirement.
381290
I have an iterative method that is good for at least 80% of these types of problems.\n\nFirst, write down the series.\n\nNext, above the line you just wrote, write the difference between each pair of elements. In this case, it will be 1, 2, 4, 8, .... In this case, the answer is obvious - they are powers of two. The next one in the differences line should be 16, so the next on the original line should be 15+16=31. This will allow you to get any member in the sequence.\n\nIf the first order of differences doesn't give rise to a discernable pattern, try the differences of differences and so on.
369017
Set one equation equal to one of the variables, then insert it into the other equation and solve for the second variable.  then insert that variable into the original equation.\n\nx+y=5 or x=5-y\nx+2y=6\n\nput x=5-y into the second equation\n\n5-y+2y=6 \n\nnow solve for y\n\ny=1\n\nput this back into one of the original equations\n\nx+1=5\n\nx=4
925629
polyeig(-5,-2,4,2) \n\nwill solve the equasion.  To learn about interpelations type:\n\nhelp interp1
967368
Just treat all other letters as constants. You can multiply, divide, add and subtract both sides of an equation and maintain the equality.
121228
here is a simple program algo\n\nprogram quad\nbegin\nvar\n     declare variables;\nget variable values of a,b,c for equation ax2+bx+c=0\nd=)b*b)-4*a*c;\nif(d<0)\nbegin\n\n   root are imaginary;\nend\nelse\n\n    root1=b(sqrt(d))/2a;\n    root2=-b(sqrt(d))/2a;\n ( note : formula i am not sure make changes as per required)\nprint the value of root1 and root2;\nend
681236
Multiply each term in the first () by each term in the second ():\n\n2x times 2x = 4x^2\n2x times 1 = 2x\n-3 times 2x = -6x\n-3 times 1 = -3\n\nThen combine 2x and -6x\nAnswer: 4x^2 - 4x - 3
576570
algebra...usually (well i do) set up a equation for everything, and solve for the variable. If u need help u can always get help in www.algebra.com .....
518727
Multiply the first equation by 2.\n\nSubtract the second equation from the new first equation.\n\nSolve for y.\n\nTake your value for y and substitute it into the original first equation.\n\nSolve for x.
347066
ok, i think one will be where you have to solve a word problem dealing with alegebra. One with number sentences that have a letter on one side of the problem and letters on both sides of the problem. i could be wrong, but i'm trying to help.
148434
So, continuing with mr_w's excellent example, we have 4 equations in 4 unknowns. So you can set this up as a matrix-vector problem.  Define matrix M such that M * Number of games bought vector = Cost & total games vector.  Assigning the rows of M in order to the total cost, the PS3 and Xbox360 cost, the PS1 and Xbox360 cost, and the total number of games, \nM = \n70 150 300 450\n0 0 300 450\n70 0 0 450\n1 1 1 1\nNumber of games bought vector =\na\nb\nc\nd\nand Cost & total games vector =\n13910 12000 3050 54\nThe solution will find the values of a, b, c and d.\nWhen I ran the solution I ended up with noninteger values for each and the values checked with the problem statements.  I hope those values were mr_w's solution.
951948
When I do word problems, I break it down into manageable chunks.  After reading the entire problem once to get a sense of what I'm dealing with, I re-read each sentence one at a time and try to write down in mathematical terms what each sentence is saying.  Often each sentence is only a portion of the overall equation, but I find if I tackle it like this, I can piece together the overall equation by looking at all the partial equations I got from each sentence.\n\nHope this helps a little.  Good luck!\n\n~ ♥ ~
784670
The trick is that you can do the same thing to both sides of an equation:\n\n1. Divide both sides by W: L = A/W\n\n2. Subtract 32 and multiply by 5/9: C = (F - 32) * 5 / 9\n\n3. Multiply both sides by 2 and divide by b: h = 2A/b\n\nSimple steps, once you have the hang of it.
769028
I would make two equations first. \nLet x= hotel\nLet y=car\nThe first equation would be\n360=3x+2y\nThe second equation would be\n500=4x+3y\n\nThen you could use linear combination, substituition, or graphing to solve. I'll use Linear Combination.\n\n360=3x+2y\n500=4x+3y\nYou want to get the x's or y's to cancel. I'll multiply the first equation by -3 and the second equation by 2. This will make the y's cancel\n\n-3(360=3x+2y)=  -1080= -9x-6y\n2(500=4x+3y)=   1000=8x+6y\n\nThe y's cancel\n-1080= -9x\n 1000=8x\n\nTHen combine the like terms\n-80= -x\n\nDivide by negative 1 and x=80\n\nThen sub in 80 for x in one of the equation and solve for y\n360=3(80)+2y\ny=60\n\nCheck you answers\n360=3(80)+2(60)\nand\n500=4(80)+3(60)\n\nHope that helped!
106013
y = -2x + 8\n\nsolve it yourself
865937
w=x\nl=2x\n2w+2l=P\n2x+2(2x)=2\n2x+4x=2\n6x=2\nx= 1/3\n\nwidth is 1/3 and length is 2/3
461929
6x=2y\ndivide both sides by 2\n3x=y\nrewrite\ny=3x