How do you solve a system by addition in algebra?
824262
well... imagine 2 functions\n\n2x + 3y = 5\n-2x + 2y = 10\n\nadd the two togather\n\n5y = 15\ny=3\n\nplug y into one of the first equations\n\n2x + 3y = 5\n2x + 3(3) = 5\n2x + 9 = 5\n2x = -4\nx = -2 and y = 3\n\nyou can check it with the other equation too\n\n-2x + 2y = 10\n-2(-2) + 2(3) = 10\n4 + 6 = 10\n10 = 10\n\nand the system is solved... \n\nx = -2 and y = 3
883726
when multiplying, exponents with like bases add, therefore\nn+1+n-1 =2n and your answer is x^2n
201908
Ah, systems.\n\nthe first problem- there are many ways you can choose to do this, but I think we should multiply both sides of the first equation by two so that they positive and negative y's will cancel out.\n\nSo now we have:\n2(2x + y)=2(4)\n3x - 2y = -1\n\nSimplified:\n4x + 2y = 8\n3x - 2y = -1\n\nnow you add down, so you get:\n7x +0y = 7\n7x =7\nx=1\n\nsubstitute 1 for x in any equation:\n2(1)+y = 4   \n2 + y = 4\ny = 2\n\n\n\nfor the second one- lets cancel out the y's again.\n\n5x - 3y = 14\n-3(2x - y) = (6)-3\n\n5x - 3y = 14\n-6x +3y = -18\n\nAdd them together:\n-x = -4\nx = 4\n\nThen solve for y:\n5x - 3y = 14\n5(4) - 3y = 14\n20 -3y = 14\n-3y = -6\ny = 2
702715
I know this can be done with matrix operations, but as I understand it, it represents the following system of equations which can be solved using junior algebra methods:\n\n-10x + 11y - z = -3\n14x  +  9y + 8z = 2\n12x  - 2y - 11z = 3\n\nAdding 8*first equation to second, gives \n-66x + 97y = -22\nSubtracting 11*first from third gives\n122x - 123y = 36, and I begin to see why one might try something different!\n\nThese last two give \nx = 393/1858\ny = -77/929  and then sub in the first to get\nz = -50/929\n\nPersonally, I don't believe it, but that's what I got.  How about you?
333726
Perform operations in this order:\ni)   brackets\nii)  powers\niii) divide\niv)  multiply\nv)   add\nvi)  subtract\n\nSo work it out like this:\n\n2 + 2 (4 - 6 * 7) + 4\n= 2 + 2 (4 - 42) + 4\n          By doing multiplication 6 * 7 in brackets first.\n= 2 + 2 (-38) + 4\n          By doing subtraction 4 - 42 in brackets.\n= 2 + -76 + 4\n          By doing multiplication 2 * -38\n= 2 - 76 + 4\n          Since + and - sign in front of 76 combine into a -\n= -74 + 4\n          By doing subtraction 2 - 76\n= -70\n          By doing addition -74 + 4
689072
5x + 3y = 16 ------ equation 1\n\n2x + 3y = 1 ------- equation 2\n2x = 1 - 3y\nLet x = (1-3y) / 2 \n\nReplace x with y in equation 1, and solve y\n\n5 [ (1-3y) / 2 ] + 3y = 16\n5 (1-3y) + 6y = 32\n5 - 15y + 6y = 32\n9y = -27\ny = -3\n\nReplace the value of y to solve x\n \ntherefore x = [ 1 - 3(-3) ] / 2\nx = 10/2 = 5\n\nYou can try and solve the other pair of system using the same basis as above.
731670
(-4x3 + 3x2 - 5) + (x2 - 5x + 6) =\n-4x3 + 3x2 - 5 + x2 - 5x + 6 =\n-4x3 + 4x2 - 5x + 1
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
1160760
what you have is something like\na(b+c)\n\nthe solution is \nab+ac\n\n(x^3)(2x^-2)+(x^3)(4x)\nnow to multiply x^a * x^b you get x^(a+b)\n\n2x^((3+(-2))+4x^(3+1)\n\n2x+4x^4
572480
breaking it apart, we have:\n\n(x+1)^3=(x+1)(x+1)(x+1)=\n(x^2 + 2x + 1)(x+1) =\n(x^3 + 3x^2 + 3x + 1) SO\n6(x+1)^3 = 6(x^3 + 3x^2 + 3x + 1) = 6x^3 + 18x^2 + 18x + 6\n\n(x+1)^2 = (x+1)(x+1)=\nx^2 + 2x + 1   SO\n-3(x+1)^2 = -3(x^2 + 2x + 1)=\n-3x^2 - 6x - 3\n\n4(x + 1) = 4x + 4\nand -9 stays the same.\n\nSo putting everything together, you have\n(6x^3 + 18x^2 + 18x + 6) + (-3x^2 - 6x - 3) + (4x + 4) - 9 \ncombine like terms and you get:\n6x^3 + (18x^2 -3x^2) + (18x - 6x + 4x) + (6 - 3 + 4 - 9)\n6x^3 + 15x^2 +  16x - 2\n\nWHEW!  That took me back to college pre-calc!
25290
If you're looking for a simple polynomial expansion, you follow this simple rule: (A+B)(C+D)=AC+AD+BC+BD. In your case, 8x*3x+8x*(-1)+5*3x+5*-1. Solving, this becomes: 24x^2-8x+15x-5\nGrouping like terms: 24x^2 + 7x - 5 .\n\nIf you're solving for x, set each term = 0. In other words: 8x+5=0 and 3x-1 = 0. Solving, x=-5/8 and x=1/3.
984158
The general approach is to move the x's to one side of the equation and the numbers to the other side, then solve for x. In your example:\n\n5x - 6 = 4x -+ 8\nFirst step: move 4x to left side. Since you can subtract the same amount from both sides of an equation the detailed step looks like this:\n5x - 6 - 4x = 4x + 8 - 4x\nor, in short form,\n5x - 4x - 6 = 8\n\nThen, move the 6 to the other side by adding 6 to both sides:\n5x - 4x - 6 + 6 = 8 + 6\nor, in short form:\n5x - 4x = 8 + 6\n\nThen, reduce both sides of the equation:\nx = 14\n\nHope this helps!
385232
If you're talking about algebra I, you are probably dealing with quadratic expressions like the following:\n\nx^2 + 7x + 6\n\nThese are a bit like a puzzle.  If the number in front of the x^2 term is 1 (as in the above example) then the puzzle is like this:\n\nLook at the 7 and the 6.  What two numbers multiply to 6 and ad to 7?\n\nConsider all the pairs of numbers that multiply to 6\n\n1,6 or 2,3.  Which pair adds to 7? The 1 and 6.\n\nSo the above equation factors to (x + 6)(x + 1)\n\nAnother example is x^2 - 6x - 16\n\nThe ques ion becomes what two numbers multiply to -16 and add to -6.\n\nThe pairs of factors of -16 are \n+ or - 1 and 16\n+ or - 2 and 8\n+ or - 4 and 4\n\nWhich pair of these factors add to -6?  With a little checking you can see the pair is -8 and +2\n\nSo this equation factors to\n(x - 8)(x + 2)\n\n\nThis even works for equations like the following:\nx^2 - 16\n\nWhat you have to remember is that this can be re-written as\n\nx^2 + 0x -16\n\nSo, what multiplies to -16 and add to zero.  Use the last example and you should see this one for yourself.\n\nGood luck.
551906
Add each equation\nA + B = 3x^2 + 2x - 2\nA - B = -x^2 + 4x - 8\n2A = 2x^2 + 6x - 10\nDivide each side by 2\nA = x^2 + 3x - 5\nNow plug into one of the original equations to get B\nB = 3x^2 + 2x - 2 - (x^2 + 3x - 5)\nB = 2x^2 - x + 3
727014
start with the O... they are always -2\nsince there are 2, and the compound must balance...\nPb must be +4\n\nso you get +4 -2
924424
The equations:\n(a+b)^2=a^2+2ab+b^2\nA^2-B^2=(A+B)(A-B)\nJames Chan's solutions were right.
1174662
2(x-4y+1)+3(-2+y-2)\n2x-8y+2-6+3y-6\n2x-8y+3y-6-6\n2x-5y-12\n\n2x-5y-12= answer\n\nHope this helps you.