# SOLUTION: I have started the problem but am lost as to how to continue. 4x &#8722; y = 2 8x + 10y = &#8722;4 This was the problem I was given and was asked to use the Gauss-Jordan met

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 Click here to see ALL problems on Matrices-and-determiminant Question 472276: I have started the problem but am lost as to how to continue. 4x − y = 2 8x + 10y = −4 This was the problem I was given and was asked to use the Gauss-Jordan method to find the solution to the system of equations. So far I did the first step but I need help understanding the steps that follow.Found 3 solutions by stanbon, Theo, MathLover1:Answer by stanbon(57967)   (Show Source): You can put this solution on YOUR website!4x − y = 2 8x + 10y = −4 ---------------- Subtract 2 times the 1st equation from the 2nd to get: 4x - y = 2 0x +12y=-8 ---- Divide thru the 2nd equation by 12 to get: 4x - y = 2 0 + y = -2/3 ---- Add the 2nd equation to the 1st to get: 4x + 0 = 4/3 0 + y = -2/3 ----- Divide thru the 1st equation by 4 to get: x + 0 = (1/3) 0 + y = (-2/3) ==== That is the final answer: Cheers, Stan H. Answer by Theo(3504)   (Show Source): You can put this solution on YOUR website!```your original equations are as follows: 4x − y = 2 8x + 10y = −4 your matrix would look like the following: 4 -1 2 8 10 -4 multiply the first row by 2 and subtract it from the second row to get: 4 -1 2 0 12 -8 divide the second row by 12 and add it to the first row to get: 4 0 16/12 0 12 -8 multiply the first row by 1/4 and multiply the second row by 1/12 to get: 1 0 4/12 0 1 -8/12 your answer should be x = 4/12 and y = -8/12 plug those values into your original equation to get: 4x − y = 2 8x + 10y = −4 become: 16/12 - (-8/12) = 2 32/12 - 80/12 = -4 these become: 24/12 = 2 -48/12 = -4 these become: 2 = 2 -4 = -4 the original equations are confirmed to be true, establishing the solutions as good. the gauss-jordan method takes gaussian elimination method one step further by making the elements on the left hand side of the matrix all equal to 1. this eliminates having to go back and solve for each of the variables in turn. ``` a reference on the gauss-jordan elimination method is shown below. http://ceee.rice.edu/Books/CS/chapter2/linear44.html Answer by MathLover1(6812)   (Show Source): You can put this solution on YOUR website! first write down your matrix then open this link to see the steps http://imageshack.us/photo/my-images/846/capture720201180502am.jpg/ so, solutions are: and