solve this linear equation:2(ax-by)+(a+4ab),2(bx+ay)+(b-4a)?
541939
doesn't make sense...incomplete.....
21539
If you have a system of equations with two variables of the form ax + by = c, dx + ey = f, where a,b,c,d,e,f are the coefficients, and x and y are variables, you can set up the equation as \n\n[a b][x] = [c]\n[d e][y] = [f]\n\n(ignore the fact there are two equals signs there, they're only there for formatting reasons)\n\nwhere the square brackets are a crude attempt on by behalf to 'draw' matrices and column vectors.\n\nTo solve the system you need to find the inverse of the matrix of the right hand side (assuming it's invertible to begin with), and "right multiply" (that is multiply from the right of each side of the equation) both sides of the equation.\n\nThat should give you:\n\n[1 0][x] = [ inverse of matrix ][c]\n[0 1][y] = [ ........................ ][f] \n\nThen it's just a matter of performing the calculation.\n\n(sorry for the crappy formatting of the post)
753426
X2   5x - 4y = 1\n10x -8y =2\n-10x + 8y = -3\n-------------------------\n  0=-1                NO SOLUTION
805693
#1\n4x+1+3=0\n4x+4=0\n4x=-4\nx=-1\n\n#2\n2y+7+4=y\n2y+11=y\ny=-11
374296
First, simplify [a(b+c)=ab+ac]\n +8x -8 +3x = -8x\nSecond, combine like terms on each side [ax+bx=(a+b)x]\n +11x - 8 = -8x\nThird, isolate a variable [if a=b, then a+c = b+c]\n 19x - 8 = 0\n 19x = 8\nFourth, eliminate coefficient [if a=b, c =/= 0; a/c = b/c]\n x = 8/19\nFinally, evaluate.\n 8([8/19]-1) + 3(8/19) = -8(8/19)\n 8(-11/19) + (24/19) = -64/19\n -88/19 + 24/19 = -64/19\n True
134065
Your statement translates to the following algebraic equation.\na+b=a-b=a*b\nSolving a+b=a-b, we get b = 0; \nSubstituting b=0 and solving a+b=a*b, we get a = 0;\nSo the two numbers are zeroes.
700872
d sin ax=a*cos ax dx\nd bx = b dx
230663
you need imaginary numbers to solve this one. Use the quadratic formula to solve ax^2 + bx + c = 0:\n\nx = -b +- sqrt(4ac)\n\nin this case:\na=1, b=2, c=-1\n\nso x has two solutions:\nx=-2+i  or x= -2-i \nwhere i=sqrt of -1 (the unit imaginary number)
929562
∫ax(2 -x)dx\n= ∫(2ax - ax²)dx\n= 2a * ½x² - a * ⅓x³ + c\n= ax² - ⅓ax³ + c
508029
The equation is:\n(x+a+b+c)^2 = 2x^2+(x+a)^2-(x+b)^2-(x+c)^2\nA simple rearrangement yields\n(x+a+b+c)^2 - x^2 = (x+a)^2-(x+b)^2 + x^2-(x+c)^2\nFactorize using the identity a^2-b^2=(a+b)(a-b)\n(x+a+b+c+x)(x+a+b+c-x) = (x+a+x+b)(x+a-x-b) + (x+x+c)(x-x-c)\nwhich can be written as\n(2x+a+b+c)(a+b+c) = (2x+a+b)(a-b)-c(2x+c)\n==> 2x(a+b+c)+(a+b+c)^2 = 2x(a-b)+(a-b)(a+b)-2xc-c^2\n==> 2x(a+b+c-a+b+c) = (a+b+c)^2 + a^2-b^2-c^2\n==> 4x(b+c) = a^2+b^2+c^2+2ab+2bc+2ca+a^2-b^2-c^2\n            = 2(a^2+ab+bc+ca) = 2(a+b)(c+a)\n==> x = (a+b)(c+a)/[2*(b+c)]
617358
x = (-b +- sqrt(b^2-4ac))/(2a)\n\nThis equation solves the quadratic equation, where\n\nax^2 + bx + c = 0.
794593
As line AC= line BC\nthen\n6=2x+2\nso x=2\nand then\nAB=x+1\nso AB=3
919864
1.  ax + xb\n2.  21x^3 + 24x*2y\n3.  24x^2 + 31x + 10\n4.  24x^2 - 8x - 6\n5.  40x^3 + 66x^2 + 38x + 6\n6.  x^2 - 1\n7.  x^3 - 8
1178662
a (x+y) + b (x*y) = z
940849
2x + 4y = -6\nX - 3y = 7 multiply by two\n\n2x + 4y = -6\n2x - 6y = 14\n{subtract equation 2 from equation 1}\n\n2x - 2x + 4y - (-6y) = -6 - 14\n10 y = -20 divide by 10\ny = -2\n\n\nplug into a equation \n2x - 6(-2)  = 14\n2x + 12 = 14\n2x = 2\nx = 1\n\nx = 1, y = 2
875476
(a + b - c)(a + b + c)\n((a+b)+c)((a+b)-c)\n(a+b)^2-c^2\na^2+2ab+b^2-c^2
879937
ax^2 + bx+c = 0\nax^2 + bx = -c\nx^2+(b/a)x+ ... = -c/a + ...\nx^2+(b/a)x+ (b/2a)^2 = -c/a + (b/2a)^2\n{x - (b/2a)}^2 = -4ac/4(a^2) + b^2/4(a^2)\nx - (b/2a)}^2 = + or - root{(-4ac + b^2)/4(a^2)}\nx= {-b + or - sqrt (b^2-4ac)}/2a\n\nTh