solve equations using sub. method: 3x-2y=24, 8x-3y=12?
81494
I'm getting some funky answers on these equations\n\nx= -48/7 and y= -156/7
799916
When you use the elimination method, you pretty much add both of the equations in order to eliminate and x or y.\n\nBefore using the elimination method you may have to multiply every term of one or both of the equations by some number so that equal terms can be eliminated\n\nIn this case multiply the second equation by -2\n\n-2 (2x + 3y) = -2(2)\n\n-4x - 6y = -4\n\nNow the equations can be added to eliminate x.\n\n     4x - 5y = 48\n+ -4x - 6y = -4\n   __________\n          -11y  = 44\n\nNow, solve for y.\n\n-11y / -11 = 44 / -11\n   y = -4\n\nNow plug the y back into one of the equations in order to find x.\n\n2x + 3 (-4) = 2\n2x - 12 = 2\n2x - 12 + 12 = 2 + 12\n2x = 14\n2x / 2 = 14 / 2\nx = 7\n\nSo, \ny = -4\nx = 7\n\nHope it helps!
1026680
3(-4 + 8a) = 25a -15\n-12 + 24a = 25a - 15\n25a-24a = -12 + 15\na = 3
213186
4x + 2y = 12\n\n\n2y = 12 - 4x\n\ny = -2x + 6\n\nm = -2
871743
Since we're given y = x+8, let's solve the first equation for x by plugging in y.\n\n3x*3y=y*x^2+96 <==> 3x*3(x+8)=(x+8)*x^2+96\nMove everything to one side and expand.\n(x+8)*x^2+96-3x*3(x+8) = 0\nx^3+8x^2 -9x^2 -24x + 96 = 0\nx^3 - x^2 -24x + 96 = 0\n\nThis is easiest solved by plugging in to the solver of a graphic calculator. Once you get values for x, plug in to y = x + 8 and you have values for y.
825795
OK,as the first one is already done,I am doing the rest for you\n4(2x-6)=x+2 =>8x-24=x+2  =>8x-x=2+24  =>7x=26  =>x=26/3=8 2/3  (3) 2(x+5)+1=3(x-1)+4   =>2x+10+1=3x-3+4 =>2x-3x=-3+4-10-1  => -x=-4  =>x=1  (5)x+6=4(4x-1)   =>x+6=16x-4  =>x-16x=-4-6  => -15x=-10  =>x=-10/-15=2/3 [after reducing]
769967
removing the brackets\n18+3y=4y-16-y\nsimplifying\n18+3y=3y-16\nadding 16\n34+3y=3y\nadding -3y\n34=0\nwhich is absurd\nso the equation cannot be solved
1134427
12x + 4y = 8\n(d/dx) * (12x + 4y = 8)\n12 + 4dy/dx = 0\ndy/dx = -12/4\ndy/dx = - 3
724639
2x-4y = 3.8\n3x - y = 17.7\n\nmultiply second equation by -4 so that when u add them both u will cancel the y's...\n2x-4y = 3.8\n-12x+4y = -70.8\n\nnow add them..\n\n-10x = -67\n     x = 67/10 = 6.7\n\nnow plug this x in for any one of the original equations and solve for y....\n\n2(6.7) - 4y = 3.8\n\n13.4 - 4y = 3.8\n-4y = -9.6\n   y = -9.6/-4 = 2.4\n\nso the solution is (6.7,2.4)
859008
x+8y = 60, 4x+4y = 60\n\nsubtract: first equation minus twice second equation\n     x  +  8y  =    60\n  -8x  -  8y   = -120\n  -7x = -60\nx=60/7\n\nThen plug x into one of the equations, say the first one\n60/7 +8y = 60\n8y = 60 - 60/7\n8y = 360/7\ny=45/7
753930
The most intuitive way to answer is to use Gauss-Jordan elimination, as described below.\n\n\nw + x + y + z = 24\n3w + 3x + 3y + 3z = 72\n3w - 2x - 3y + 3z  = -9\n5x + 6y= 81\n\nw + x + y + z = 24\n5w + 5x + 5y + 5z = 120\n5w + 3x - 2y - 2z  = 4\n2x + 7y + 7z = 116\n\nw + x + y + z = 24\n2w + 2x + 2y + 2z = 48\n2w + 4x + 4y - 5z  = 22\n-2x - 2y + 7z = 26\n\n2x + 7y + 7z = 116\n-2x - 2y + 7z = 26\n\n4x + 9y = 90\n5x + 6y= 81\n\n20x + 45y = 450\n20x + 24y = 324\n21y = 126\n\ny = 6\n\n4x + 9y = 90\n4x + 54= 90\n4x  = 36\nx = 9\n\n2x + 7y + 7z = 116\n18 + 42 + 7z = 116\n7z = 56\nz = 8\n\nw + x + y + z = 24\nw + 9 + 6 + 8 = 24\nw = 1\n{w,x,y,z} = {1,9,6,8}\n\nAnother method is to put the coefficiants into a matrix, and put it into reduced-row echelon form.\n\n|1 1   1  1  24|\n|3  -2 -3 3 -9|\n|5  3  -2 -2 4|\n|2  4  4  -5 22|\n\nIn RREF...\n|1 0 0 0 1|\n|0 1 0 0 9|\n|0 0 1 0 6|\n|0 0 0 1 8|\n\nThese are all new valid equations, just in a much nicer form. Specially, 1w+0x+0y+0z=1, etc.\nThis tells us that w=1, x=9, y=6, and z=8.\n\nAlso, you could use Cramer's rule with these equations and get the same answer, but I will not demonstrate that one.
86546
(3y+1)(-2)+y\n-6y-3+y\n-5y-3\n\n12s+(7-s)2\n12s+14-2s\n10s+14\n\n7x-3x(x+1)\n7x-3x^2-3x\n-3x^2+4x\n\n3t(t-5)+6t^2\n3t^2-15t+6t^2\n9t^2-15t\n\n4w^2-w(2w-3)\n4w^2-2w^2+3w\n2w^2+3w
424288
1. y2+6y+8 = (y+4)(y+2)\n2. x2+7x+12 = (x+4)(x+3)\n3. z2+2z-24 = (z-4)(z+6)\n4. x2+7x+10 = (x+2)(x+5)
679588
Multiply it out...\n2y+6y+24x-24y-6x\nThen combine\n-16y+18x OR\n18x-16y
763532
put in y=3x-8 in x+y=4 like this\n\nx+(3x-8)=4\n\n4x-8=4\n   +8  +8\n\n4x=12\n/4    /4\n\nx= 3
1144396
you would take the 2x-4y=3 and solve for a variable, such as x=(3-4y)/3   you now have what x equals and you sub that into the other equation so you now have 2[(3-4y)/3]-3y=0 and you should be able to solve that equation
851885
You have :\n | x+4y   =12\n | 2x-3y  =6\n<=>\n | 2x+8y=24  \n | 2x-3y=6              \n<=>  \n | 11y=18\n | x+4y=12\n<=>\n | y=18/11\n | x=12-4(18/11)=60/11\n\nFinally, we have (x=60/11) and (y=18/11) .\n ^_^