Show and explain EACH step in solving the following system of equations by the substitution method.?
931393
GIVEN:\n\n0.4x - 0.1y = 5 \n6.4x + 0.4y = 60\n\nSTEP 1:  Multiply the first equation by 4 to get the following:  (because notice that 0.1 * 4 = 0.4, and we will be able to cancel our y's out and solve for x)\n\n1.6x - 0.4y = 20\n6.4x + 0.4y = 60\n\nSTEP 2:  Add the two equations together, to get one equation with our x variable only:\n\n1.6x - 0.4y = 20\n6.4x + 0.4y = 60\n-----------------------\n8.0x + 0y = 80\n\nSTEP 3:  Divide both sides by 8 to solve for x:\n\nx = 10\n\nSTEP 4:  Substitute this value for x into either one of your original 2 equations to solve for y:\n\n0.4x - 0.1y = 5\n0.4(10) - 0.1y = 5\n4 - 0.1y = 5\n-0.1y = 1\n0.1y = -1\ny = -10\n\nFINAL STEP:  Your answers are x = 10, y = -10\n\nHope that helped!\n\n~ ♥ ~
971390
{3XY^2M/1}-{2M/[X^-1Y^-1]^2\n+{[4X^2Y^2]/M^-1}-\n(3X^(3Y)^(3M)^-1/(XYM)^-2
27501
Start out by multiplying the\n            first equation by -1 and add\n            it to the second equation to \n            eliminate x from the second\n            equation.\n\n            -x  - y - z = -4\n             x - 2y - z = 1\n            ----------------\n               -3y - 2z = -3\n\n            Now eliminate x from the third\n            equation by multiplying the first\n            equation by -2 and add it to\n            the third equation.\n\n            -2x - 2y - 2z = -8\n             2x -  y - 2z = -1\n            ------------------\n                 -3y - 4z = -9\n\n            Next, eliminate y from the third\n            equation by multiplying the second\n            equation by -1 and adding it to\n            the third equation.\n\n             3y +  2z = 3 \n            -3y -  4z = -9\n            --------------\n                  -2z = -6\n\n            Solve the third equation for z.\n                 \n            -2z = -6\n              z = 3\n\n            Substitute 3 for z in the\n            second equation and solve for y.\n\n            -3y - 2z = -3\n            -3y - 2(3) = -3\n            -3y - 6 = -3\n            -3y = 3\n            y = -1\n\n            Lastly, substitute -1 for y and\n            3 for z in the first equation\n            and solve for x.\n\n            x + (-1) + 3 = 4\n            x + 2 = 4\n            x = 2\n\n            The answer is (2, -1, 3).\n\n\nnext time, do your homework on your own.
778763
1) (a - b)(x - y)\n2) (x^9 + y^3)(x^9 - y^3)\n3) (6x + 5)(x + 8)\n4) (x - 9)(x - 7)
799504
FeS + 2HBr --> FeBr2 + H2S\nFe2+ + S2- + 2H+ + 2Br- --> Fe2+ + 2Br- + H2S\n2H+ + S2- --> H2S\n\nK2CO3 + CuCl2 --> 2KCl + CuCO3\n2K+ + CO32- + Cu2+ + 2Cl- --> 2K+ + 2Cl- + CuCO3\nCu2+ + CO32- --> CuCO3\n\npeace\nvixklen
408462
to solve such a system in general, what you do is this: take the first equation, solve it for x treating y as you would a constant. In your case, this is x = 4 + y.\n\nThen, take your expression for x and substitute it everywhere you see x in the second equation; in your case you get 3 *(4+y) + 2y = 7.\n\nSolve this now 1-variable equation for y, once you find y (in this case, -1).\n\nSubstitute the value of y into either equation, and you get the value of x (3 in this case).
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
1141591
1. 2\n\n2. 2a^2b\n\n3. 6xyz^2(2z-3y)\n\n4. 3a(4a-b+3ab^2)\n\n5.(d+2)(d+3)\n\n6.(x-9)(x-2)\n\n7. (4x-1)(x+3)\n\n8. (4b-9)(4b+9)\n\n9.(y+7)^2\n\n10. (2m+7n)^2
772697
You use the coefficients and the answers to get a 2X3 matrix:\n1 1 8\n1-1 4\n\nAdd row 1 to row 2 to get a new row 2 with a zero in it:\n\n1 1 8\n2 0 12\n\nDivide row 2 by 2 to get a 1 in it\n\n1 1 8\n1 0 6\n\nMultiply row 2 by -1 and add it to row 1 to get a new row 1:\n\n0 1 2\n1 0 6\n\nSwitch the rows:\n\n1 0 6\n0 1 2\n\nSo x is 6 and y is 2\n\nCheck by plugging into the original equations
98021
Okay, here we go:\n\nUsing the second equation you can rearrange it to solve that equation for y in terms of x so we get:\n\ny = x + 17  [ I'll call this Equation 4 ]\n\nThen using the third equation you, can obtain z in terms of y:\n\nz = -15/2*y [ Equation 5 ]\n\nSubstituting Equation 4 into Equation 5 we obtain:\n\nz = - 15/2 * ( x + 17 ) [ Equation 6 ]\n\nSo now with Equations 6 and 4 we have y in terms of x and z in terms of x.  We substitute these into Equation 1 to get:\n\nx + ( x + 17 ) + ( -15/2 * (x + 17 ) ) = 1 [Equation 7]\n\nSimplying equation 7 by multiplying things out and combining terms of x we get:\n\n-11/2 * x - 221/2 = 1 [Equation 8]\n\nAnd finally isolating x gives:\n\nx = -223/11 ~= -20.272727272727\n\nNote that we also know y and z in terms of x, so figuring them out is trivial:\n\ny = x + 17 = -233/11 + 17 = -36/11 ~= -3.2727\nz = -15/2 * (x + 17) = -15/2 * ( -233/11 + 17 ) = 270/11 ~= 24.545454\n\nDoes that method make sense?  We used the substitution method to obtain this answer.  Try another one for yourself to make sure you understand!
268070
Check out this site. It gives you a few examples. It was helpful for my cousin when she was leaning how to do them.\nhttp://www.purplemath.com/modules/solvelin.htm
999333
There are several simple rules for re-arranging and solving equations.  It would be in your best interest to try and learn them, they aren't very hard.
695176
6x^2-3x-4x+2\n3x(2x-1)-2(2x-1)\n(2x-1)(3x-2)
859187
I'll do one for u.\nIn the first,\nMultiplying both sides by x*,we get\nx+3x+2x*=7x*\n4x+2x*=7x*\nMoving 4x and 2x* to the R.H.S.\n5x*-4x+0=0\nThus 5x*-4x=0\nAttempt the others in the same manner.
958006
in order to solve the system of equations you can do one of two things.  The easiest thing to do is to set the two equations to be equal. i.e. \n\nsince y=2x and y = -3x+5, then 2x=-3x+5.  In solving for x you will find that 5x=5 or x=1.  Then you can plug your resulting x back into the equation to get y=2(1) =2.  The main thing you are trying to do is get one of your variables to be equal to some combination of your other variables.  For example, if you are trying to solve 3y+2x-1=5x+3 and 6y=2x+7.  The first thing you want to do is to get a single variable by itself on one side of an equation.\nLet's start with the first equation, 3y+2x-1=5x+3. You would try to group the y terms by themselves on one side of the equation, an group the x terms and constants on the other side of the equation.  In this example, in order to group the terms correctly, you would have 3y=3x+4.  Then solve for y by itself by dividing both sides by 3.  The result is y=x+4/3.  You take this result and substitute for y in the second equation, 6y=2x+7.   You will get 6(x+4/3)=2x+7.  Then you solve for x by itself.  6x+8=2x+7\n4x=-1;  x=-1/4.  Then you can substitute this result back into either of your original equations to produce your solution for this system.  6y=2(-1/4)+7 => 6y=13/2 =>y=13/12.  In order to check your answer, you can graph the two linear equations.  Where the two lines intersect is the solution to your system.\n\n\nIf you are looking for a more advanced way to solve a system of equations, then you may want to consider using an augmented matrix.  Rearrange your equations so that you have only variables on one side of your equations, and only constants on the other side of your equations, then sole the system of Ax=b.  The matrix A is the coefficients of your variables, and b is a vector of your constants.  x is a vector of your variables.  Augment the matrix of your coefficients with your constant vector and do Gaussian Elimination until the matrix is in reduced row echelon form.  This will provide the exact solution to the system of equations.
589722
Step 1: Solve one equation for one variable in terms of the other.\nStep 2: Plug that into the other equation and solve for the second variable.\nStep 3: Plug the second variable into the first equation and solve for the first variable.
789649
We'll use the "addition" (or "elimination") method, but if we were to use the substitution method, we'd get the same result.\n\nIf you multiply both sides of the first equation by 3, you'll get:\n\n9x - 9y = 27\n\nAdding the two equations together then produces:\n\n9x - 9y - 9x + 9y = 27 - 25\n\nWhen you combine like terms, you get\n\n0 = 2\n\nNow, obviously, that's not true, which means this is an "inconsistent system" -- a system without any solutions.\n\nHope that helps!