document.write( "Question 1196448: I've been working on this for hours, but keep taking the wrong path. I need to solve the 4x4 equations:
\n" ); document.write( "2w + x - y + 2z = 10
\n" ); document.write( "-w - 3x + y - 5z = -11
\n" ); document.write( "3w + 5x - 3y + z = 35
\n" ); document.write( "-4w - 2x - 3y - z = 2 \n" ); document.write( "

Algebra.Com's Answer #829431 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!
I've been working on this for hours, but keep taking the wrong path. I need to solve the 4x4 equations:
\n" ); document.write( "2w + x - y + 2z = 10
\n" ); document.write( "-w - 3x + y - 5z = -11
\n" ); document.write( "3w + 5x - 3y + z = 35
\n" ); document.write( "-4w - 2x - 3y - z = 2
\n" ); document.write( "

DO NOT bother to even look at that woman's RIDICULOUS method of solving this. As usual, it's complicated as HELL,\r\n" );
document.write( "with all those solutions of variables that form UNNECESSARY fractions!! She needs to learn mathematics!\r\n" );
document.write( "\r\n" );
document.write( "Looking at eqs (i) & (ii), it's obvious that \"y\" can be immediately eliminated by adding the two.\r\n" );
document.write( "Likewise, looking at eqs (iii) & (iv), it's clear that \"y\" can also be immediately eliminated by subtracting one\r\n" );
document.write( "equation from the other. So, let's do just that!\r\n" );
document.write( "\r\n" );
document.write( "  2w +  x  - y + 2z =   10 ----- eq (i)\r\n" );
document.write( "-  w - 3x  + y - 5z = - 11 ----- eq (ii)\r\n" );
document.write( "   w - 2x - 3z = - 1 ---- Adding eqs (i) & (ii) ------ eq (v)\r\n" );
document.write( "\r\n" );
document.write( "  3w + 5x - 3y +  z =   35 ----- eq (iii)\r\n" );
document.write( "- 4w - 2x - 3y -  z =    2 ----- eq (iv)\r\n" );
document.write( "  7w + 7x + 2z = 33 ----- Subtracting eq (iv) from eq (iii) ----- eq (vi)\r\n" );
document.write( "\r\n" );
document.write( "- 3w - 9x  + 3y - 15z = - 33 ----- eq (ii) ---- Multiplying eq (ii) by 3 ---- eq (vii)\r\n" );
document.write( "  3w + 5x - 3y +  z =   35 ----- eq (iii)\r\n" );
document.write( "    - 4x - 14z = 2 ---- Adding eq (vii) & (iii)\r\n" );
document.write( "    ------ Dividing by/Factoring out GCF, - 2 \r\n" );
document.write( "       2x + 7z = - 1 ----- eq (viii)\r\n" );
document.write( "\r\n" );
document.write( " w - 2x - 3z = - 1 ---- eq (v)\r\n" );
document.write( "7w + 7x + 2z = 33 ----- eq (vi)\r\n" );
document.write( "7w - 14x  - 21z = - 7 ----- Multiplying eq (v) by 7 ---- eq (ix)\r\n" );
document.write( "      21x + 23z = 40 ---- Subtracting eq (ix) from eq (vi) ------ eq (x)\r\n" );
document.write( "\r\n" );
document.write( "Now, we have 2 equations in 2 UNKNOWNS:\r\n" );
document.write( "      2x + 7z = - 1 ----- eq (viii)\r\n" );
document.write( "      21x + 23z = 40 ---- eq (x)\r\n" );
document.write( "      42x + 147z = - 21 ---- Multiplying eq (viii) by 21 ----- eq (xi)\r\n" );
document.write( "      42x +  46z = 80 ------ Multiplying eq (x) by 2 ----- eq (xii)\r\n" );
document.write( "            101z = - 101 --- Subtracting eq (xii) from eq (xi)\r\n" );
document.write( "              \r\n" );
document.write( "\r\n" );
document.write( "      2x + 7(- 1) = - 1 ---- Substituting - 1 for z in eq (viii)\r\n" );
document.write( "      2x - 7 = - 1\r\n" );
document.write( "      2x = 6\r\n" );
document.write( "      \r\n" );
document.write( "\r\n" );
document.write( "      w - 2(3) - 3(- 1) = - 1 ----- Substituting - 1 for z and 3 for x in eq (v)\r\n" );
document.write( "      w - 6 + 3 = - 1\r\n" );
document.write( "      w - 3 = - 1\r\n" );
document.write( "      \r\n" );
document.write( "\r\n" );
document.write( "      - 2 - 3(3)  + y - 5(- 1) = - 11 ----- Substituting - 1 for z, 3 for x, and 2 for w in eq (ii)\r\n" );
document.write( "      - 2 - 9 + y + 5 = - 11\r\n" );
document.write( "      - 6 + y = - 11\r\n" );
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