document.write( "Question 1205687: Solve the system of linear equation below:
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\n" ); document.write( "W + 5x + 3y + 2z = 15
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Algebra.Com's Answer #842687 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Solve the system of linear equation below:\r\n" );
document.write( "2w + 3x + y + 2z = 16\r\n" );
document.write( "W + 4x + 3y + 3z = 15\r\n" );
document.write( "3w + 2x + 4y + z = 22\r\n" );
document.write( "W + 5x + 3y + 2z = 15\r\n" );
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document.write( "FYI: \r\n" );
document.write( "This can be done by applying the system-of-equations solution, as follows:\r\n" );
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document.write( "2w + 3x +  y + 2z = 16 ------- eq (i)\r\n" );
document.write( " w + 4x + 3y + 3z = 15 ------- eq (ii)\r\n" );
document.write( "3w + 2x + 4y +  z = 22 ------- eq (iii)\r\n" );
document.write( " w + 5x + 3y + 2z = 15 ------- eq (iv)\r\n" );
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document.write( "2w + 3x +  y + 2z = 16 ------- eq (i)\r\n" );
document.write( " w + 5x + 3y + 2z = 15 ------- eq (iv)\r\n" );
document.write( " w - 2x - 2y = 1 ------ Subtracting eq (iv) from eq (i) ----- eq (v)\r\n" );
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document.write( "3w + 2x + 4y +  z = 22 ------- eq (iii)\r\n" );
document.write( "6w + 4x + 8y + 2z = 44 ------- Multiplying eq (iii) by 2 ---- eq (vi)\r\n" );
document.write( " w + 5x + 3y + 2z = 15 ------- eq (iv)\r\n" );
document.write( "5w - x + 5y = 29 ------ Subtracting eq (iv) from eq (vi) ----- eq (vii)\r\n" );
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document.write( "3w + 2x +  4y +  z = 22 ------ eq (iii)\r\n" );
document.write( "9w + 6x + 12y + 3z = 66 ------ Multiplying eq (iii) by 3 ---- eq (viii)\r\n" );
document.write( " w + 4x + 3y + 3z = 15 ------- eq (ii)\r\n" );
document.write( "8w + 2x + 9y = 51 ----- Subtracting eq (ii) from eq (viii) ---- eq (ix)\r\n" );
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document.write( " w - 2x - 2y =  1 ------ eq (v)\r\n" );
document.write( "8w + 2x + 9y = 51 ------ eq (ix)\r\n" );
document.write( "     9w + 7y = 52 ------ Adding eqs (v) and (ix) ----- eq (x)\r\n" );
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document.write( " 5w -  x +  5y = 29 ----- eq (vii)\r\n" );
document.write( "10w - 2x + 10y = 58 ----- Multiplying eq (vii) by 2 ---- eq (xi)\r\n" );
document.write( " 8w + 2x +  9y = 51 ----- eq (ix) \r\n" );
document.write( "     18w + 19y = 109 ---- Adding eqs (xi) and (ix) ----- eq (xii)\r\n" );
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document.write( "Finally, we have 2 equations in 2 variables:\r\n" );
document.write( "      9w +  7y =  52 ----- eq (x)\r\n" );
document.write( "     18w + 19y = 109 ----- eq (xii)\r\n" );
document.write( "     18w + 14y = 104 ----- Multiplying eq (x) by 2 ---- eq (xiii)\r\n" );
document.write( "            5y = 5 ---- Subtracting eq (xiii) from eq (xii)\r\n" );
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document.write( "        9w + 7y = 52 ---- eq (x)\r\n" );
document.write( "      9w + 7(1) = 52 ---- Substituting 1 for y in eq (x)\r\n" );
document.write( "             9w = 45\r\n" );
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document.write( "    5w - x + 5y = 29 ----- (vii)\r\n" );
document.write( "5(5) - x + 5(1) = 29 ----- Substituting 1 for y and 5 for w, in eq (vii)\r\n" );
document.write( "     25 - x + 5 = 29\r\n" );
document.write( "       - x + 30 = 29\r\n" );
document.write( "            - x = - 1\r\n" );
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document.write( "       3w + 2x + 4y + z = 22 ----- eq (iii)\r\n" );
document.write( " 3(5) + 2(1) + 4(1) + z = 22 ----- Substituting 1 for y, 5 for w, and 1 for x in eq (1ii)\r\n" );
document.write( "         15 + 2 + 4 + z = 22\r\n" );
document.write( "                 21 + z = 22                   \r\n" );
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document.write( "I never saw what Tutor @IKLEYN saw. Her solution is much, much shorter than mine because by using\r\n" );
document.write( "subtraction and eqs (ii) and (iv), she was able to eliminate 2 of the 4 variables. Thus, use hers\r\n" );
document.write( "if you're looking to solve this system by this method.

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