What is the answer to this system using substitution: 4x + 9y = 24 and y= -1/3x + 2?
104006
Start with \n\n    4x + 9y = 24\n\nsubstitute the value of y from the second equation:\n\n    4x + 9(-x/3 + 2) = 24\n--> 4x -3x + 18 = 24\n--> x = 24 - 18\n--> x = 6\n\nand now y can be computed,\n\n    y = -6/3 + 2\n--> y = 0
561927
Y - Y1 = M(X - X1)\n\nY - 4 = -2(x + 1)\nY - 4 = -2x - 2\n\nY = -2x + 2
386537
4y=3x\ny=3x/4\ny=3/4 x\n\nGet it?
272177
multiply both sides by 3 and you'll get\n3x-3*4=-2*(y-9)\n\n3x-12=-2y+18\n-2y+18=3x-12\n-2y=3x-12-18\n-2y=3x-30  divide both sides by -2\n\ny = (-3/2)x + 15
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?
1070900
5x - 2y + 4 = 0 (i)\n3x + 2y + 12 = 0 (ii)\n(i) + (ii)\n\n8x + 16 = 0\n8x = -16\nwherefore x = -2\n\nsub x = -2 into eq (i)\n-10 - 2y + 4 = 0\n-6 = 2y\nwherefore y = -3\n\nx = -2 y = -3 wherefore your homework is done
351633
4-y-2y=10\n4-3y=10\n-3y=6\ny=-2\n\nx=4-(-2)\nx=6
752254
Well, let's check if y=4.\nJust replace y with 4\n4(4) + 2(4) = 24\n16 + 8 = 24\n24 = 24 \nThis is equation is true, so you are correct.
867879
Just plug 0 in the function whenever you see y.\n\n4x + 3(0) + 24 = 0\n4x + 0 + 24 = 0  \n\nThen solve for x.\n\n4x = -24\nx = -6
706243
-2y+3=7y-42\n-2y+3-3=7y-42-3\n-2y=7y-45\n-2y-7y=7y-7y-45\n-9y=-45\n-9y/-9=-45/-9\ny=5
886222
Solve for one variable and plug it into the second equation...\n\nSo, let's solve the first equation for y:\n-x + y = -4\ny = x - 4\n\nNow plug this into the second equation:\n4x - 3(x - 4) = 13\n\nDistribute through the parentheses:\n4x - 3x + 12 = 13\n\nSubtract 12 from both sides:\n4x - 3x = 1\n\nSimplify:\nx = 1\n\nNow plug this back into your original substitution:\ny = x - 4\ny = (1) - 4\ny = -3\n\nSo your answer is x = 1 and y = -3.\n\nYou should double-check your answer....\n-x + y = -4,\n-(1) + (-3) =? -4  \n-4 = -4 <-- check\n\n4x - 3y = 13\n4(1) - 3(-3) =? 13\n4 + 9 = 13 <-- check\n\nSo your answer is:\nx = 1\ny = -3
287717
-4y^+8y+3y^2-6\n-4y(y^2-2)+3(y^2-2)\n(-4y+3)(y^2-2)\n\ndoes that make sense?
796461
1) x = y\nSubstituting:\n4x - 3x = -3\nx = -3\ny = -3\n\n2) 3x + 2y = 6\nx = 2y - 6\nSubstituting:\n3(2y - 6) + 2y = 6\n6y - 18 + 2y = 6\n8y = 24\ny = 3\nx = 2(3) - 6\nx = 0\ny = 3\n\n3) 2x - 6y = 2\n-3x + 9y = -3\nIf you divide the top by 2 and the bottom by -3 you get:\nx - 3y = 1\nx - 3y = 1\n\nThese are equivalent, so you can't determine a single solution.\n\nThe best you can do is simplify the equation to get a formula for y given x:\n3y = x - 1\ny = (1/3)x + (-1/3)\nBecause you can't isolate a single variable, you essentially have one equation and two unknowns.  The solutions will lie along the line with a slope of 1/3 and a y-intercept of -1/3.
826575
Use one equation to substitute into the other,then solve for a one variable problem.  Use your new information (the solved variable) to solve for the second variable.\n\nFor the first set:\n\n-3x - y = 2 rearranged becomes:\ny = -3x -2\n\nUsing this "definition" of y, substitute it into the second equation as such:\n\n-6x + 2(-3x -2) = -2\n-6x - 6x - 4 = -2\n-12x = 2\nx = -1/6\n\nSubstitute -(1/6) for x in either equation to solve for y:\n\n-3(-1/6) - y = 2\ny = -3/2\n\nDo the same for the second pair of equations to make sure you got it (the answers for x and y are x=9/7, y = 1/7).
1170681
4y+228=352\n4y=352-228\n4y=124\ny=124/4\nTherefore y=31\nAnswer is B.
897443
2x + y = - 9\n\n2x + y - y = - 9 - y\n\n2x = - 9 - y\n\n2x/2 = - 9/2 - y/2\n\nx = - 9/2 - y/2\n\n- - - - - - - -\n\ny values\n\n2x + y = - 9\n\n2x + y - 2x = - 9 - 2x\n\ny = - 9 - 2x\n\n- - - - - - - - - - - - -\n\n2).\n\nx values\n\n-x - y = - 8\n\n- x - y + y = - 8 + y\n\n- x = - 8 - y\n\n- 1(- x) = - 1(- 8) + (- 1)(y)\n\nx = 8 - y\n\n- - - - - - - - - - - -\n\ny values\n\n- x - y = - 8\n\n- x - y + x = - 8 + x\n\n- y = - 8 + y\n\n- 1(- y) = -1(- 8) + (- 1)(x)\n\ny = 8 - x\n\n- - - - - - - - - - - -\n\n3).\n\nx values\n\n- 3x + 4y = 2\n\n- 3x + 4y - 4y = 2 - 4y\n\n- 3x = 2 - 4y\n\n- 3x/ - 3 = 2/- 3 - 4/- 3\n\nx = - 2/3 + 4/3\n\n- - - - - - - -\n\ny values\n\n- 3x + 4y = 2\n\n- 3x + 4y + 3x = 2 + 3x\n\n4y = 2 + 3x\n\n4y/4 = 2/4 + 3x/4\n\ny = 1/2 + 3x/4\n\n- - - - - - - - - -\n\n4).\n\nx values\n\n- 2x - y = - 3\n\n- 2x - y + y = - 3 - y\n\n- 2x = - 3 - y\n\n- 2x/ -2 = - 3/- 2 - y/-2\n\nx = 3/2 + y/2\n\n- - - - - - - - - \n\ny values\n\n- 2x - y = - 3\n\n- 2x - y + 2x = - 3 + 2x\n\n- y = - 3 + 2x\n\n- 1(- y) = -1 (- 3) + (- 1) (2x)\n\ny = 3 - 2x\n\n- - - - - - - -s-
275027
Solve for y in the first equation and then substitute into the second equation.\n4x + 2y = 0  Subtract 4x from each side\n2y = -4x  Divide both sides by 2\ny = -2x\nSubstitute -2x for y in the equation 6x + 3y = 0\n6x + 3(-2x) = 0\n6x - 6x = 0\n0 = 0\nThis means there are infinitely many solutions of the form (x,y) where x is any real number and y = -2x.\nTherefore, the answer is\n(x,-2x), where x is any real number.