x and y are real numbers...if x+y=0,then how do i prove that x=-y?
89742
x and y are real numbers...if x+y=0,then how do i prove that x=-y?\nJust transfer the y variable to the right side of the first equation.\nx=0-y.\nAnd then you can just take out the zero.\nAnd you get x=-y
399118
y-int= (0,-5)\nx-int= (-1.2,0)
266936
Counterexample: 1\n\nJay's proof is false because x(x-1) = 0 just says that x could be either 1 or 0 to satisfy that equation. x was 1 in that case. It does not mean that 1=0.\n\nJZ-LP's proof is false because you can't say let 1=0.\n\nBianca is just plain wrong.
955603
x+0=x is always true. This is the definition of the identity property of addition.
803771
sq.rt of x*y = Sq.rt X * sq.rt. Y\n\nIt can be proven that:\n √(x*y) = √x * √y\n\nConsider the first part → √(x*y).\nTwo number values, one is x and the other is y, they are multiplied together.  You then take the square root of this result.\n\nConsider the second part → √x * √y.\nYou take the square root of x and y and then you multiply the results together.\nIt can be shown that the results of the first part is the same as the result of the second part.
240934
Solution: y = 9 - x or y = -x + 9\n\nHere are the steps I took:\nThe equation must equal y = mx + b, so we start with:\n1. x + 2y = 18\n2. x + y = 9 (Divide both sides by 2 to remove it from the "y")\n3. y = 9 - x (Subtract "x" from both sides)\n\nIn this type of equation in algebra, you have to produce steps to isolate the "y".
500255
This is called an inequality. First, find the zeros (in this case, -4 and 9). Next, make a number line:\n<------(-4)----------(9)----->\nNow, determine where inside and outside the zeros the inequality will be true or false. Finally, express your answer in terms of the inequality.\nExample: x+12 > 0\nAnswer: x > -12
793917
1)x+y-z=0.........(eqn. 1)\n2x-y+z=3...........(eqn. 2)\n4x+2y-2z=-2       (eqn.3)\nMultiplying eqn.1 by by 2 and subtracting it from eqn.2,we get\n-3y+3z=3...........(eqn. 4)\nMultiplying eqn.2 by 2 and subtracting it from eqn.3,we get\n4y-3z=-4...........(eqn 5)\nAdding eqn, 4 and 5 we get,y=7\nPutting the value of y in eqn 4 .we get\n-21+3z=3 or,3z=24  or z=8\nputting the value of y and z in eqn.1,we get\nx+7-8=0 \n=>x-1=0 or x=1\nTherefore,x=1.y=7 and z=8  ans\n2)x+2y=9....(eqn 1)\n 2x-3y=4     (eqn.2)\nmutiplying eqn.1 by 2 and subtracting it from eqn 2,we get\n-7y=-14 or y=2\nPutting the value of y in eqn 1,we get.\nx+4=9 or x=5\nTherefore x=5 and y=2 ans.
1142461
1. x-y=5; y= x - 5\nAdd y to each side x - y + y = 5 + y, becomes x = 5 + y. Subtract 5 from each side, x - 5 = 5 - 5 + y, becomes x - 5 = y\n\nSolve the rest on your own
735754
just plug the numbers in.  if y=8, and x=2, \nits 8=a(2^2)\nso 8=a(4)\nso a=2.\nhope that helps!
421674
y = (x mod 5) + 1.\n\nThough that does seem a bit like cheating :)
1119654
(a+b)(a-b)=b(a-b),\nhere you want divide both sides by a-b,\nbut this is not accepted,\nbecause a-b=0 (as you have assumed that a=b)\nDivision by 0 is not defined.\nDividing both sides by 0 is your mistake.
909284
((1/x) + (1/y)) / ((1/x) - (1/y))\n\n((y + x)/xy) / ((y - x)/xy)\n\n((y + x)/xy) * ((xy)/(y - x))\n\n(xy(y + x))/(xy(y - x))\n\n(y + x)/(y - x) = (x + y)/(-x + y) = (x + y)/(-(x - y)) = -(x + y)/(x - y)
748852
yes the signs have just been changed\ntake -x+y=-2 and multiply by -1 on both sides\n \nyou get x-y=2 and since the same thing was done to both sides the equation is equivalent
973577
given x < y\n\nnot sure if this would be using mathmatical induction but this is how i would do it\n\ntake\nx < 1/2 (x+y) < y\n2x< x + y < 2y\nx < y < 2y\n\nx<y is stated to be true and 2y is certainly bigger than y\ntherefore x < 1/2 (x+y) < y
88953
=\na(x-y)+x(x-y)\n=(a+x)(x-y)\ndone
866301
because y- x > 0\n\n|y-x | = y- x (positive value)\n\nx-y < 0\n\nso | x-y| = y-x (as absolute value positive)