document.write( "Question 1135198: Solve the following equations simultaneously.
\n" ); document.write( "5x - 6y + 4z = 15
\n" ); document.write( "7x + 4y - 3z = 19
\n" ); document.write( "2x + y + 6z = 46
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Algebra.Com's Answer #752762 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"5x+-+6y+%2B+4z+=+15\"$ .........eq.1
\n" ); document.write( " $\"7x+%2B+4y+-+3z+=+19\"$ .........eq.2
\n" ); document.write( " $\"2x+%2B+y+%2B+6z+=+46\"$ .........eq.3
\n" ); document.write( "--------------------------------------------------\r
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\n" ); document.write( "\n" ); document.write( "start with\r
\n" ); document.write( "\n" ); document.write( " $\"7x+%2B+4y+-+3z+=+19\"$ .........eq.2.......both sides multiply by $\"2\"$
\n" ); document.write( " $\"2x+%2B+y+%2B+6z+=+46\"$ .........eq.3
\n" ); document.write( "----------------------------------------------
\n" ); document.write( " $\"14x+%2B+8y+-+6z+=+38\"$ .........eq.2
\n" ); document.write( " $\"2x+%2B+y+%2B+6z+=+46\"$ .........eq.3
\n" ); document.write( "-------------------------------------------------add both\r
\n" ); document.write( "\n" ); document.write( " $\"14x+%2B+8y+-+6z+%2B2x+%2B+y+%2B+6z=+38%2B46\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"16x+%2B+9y+=+84\"$ ........solve for $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"16x+=+84-9y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+84%2F16-9y%2F16\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+21%2F4-9y%2F16\"$ ............eq.1a\r
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\n" ); document.write( "\n" ); document.write( "go to\r
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\n" ); document.write( "\n" ); document.write( " $\"5x+-+6y+%2B+4z+=+15\"$ .........eq.1
\n" ); document.write( " $\"2x+%2B+y+%2B+6z+=+46\"$ .........eq.3......both sides multiply by $\"6\"$
\n" ); document.write( "--------------------------------------------------
\n" ); document.write( " $\"5x+-+6y+%2B+4z+=+15\"$ .........eq.1
\n" ); document.write( " $\"12x+%2B+6y+%2B+36z+=+276\"$ .........eq.3
\n" ); document.write( "---------------------------------------------------add both\r
\n" ); document.write( "\n" ); document.write( " $\"5x+-+6y+%2B+4z+%2B12x+%2B+6y+%2B+36z+=+15%2B276\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"17x++%2B+40z+=+291\"$ .......solve for $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"17x++=+291-40z+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x++=+291%2F17-40z%2F17+\"$ ............eq.1b\r
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\n" ); document.write( "\n" ); document.write( "from eq.1and eq.1b we have\r
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\n" ); document.write( "\n" ); document.write( " $\"+21%2F4-9y%2F16=291%2F17-40z%2F17\"$ .......sole for $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+40z%2F17=291%2F17-21%2F4%2B9y%2F16\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+40z%2F17=9y%2F16+%2B+807%2F68\"$ ........both sides multiply by $\"17\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+40z=17%289y%2F16%29+%2Bcross%2817%29%28+807%2Fcross%2868%294%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+40z=153y%2F16+%2B+807%2F4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+z=+153y%2F640+%2B+807%2F160\"$ .............eq1c\r
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\n" ); document.write( "\n" ); document.write( "go to $\"2x+%2B+y+%2B+6z+=+46\"$ .........eq.3, substitute $\"x\"$ from eq.1a and $\"z\"$ from eq.1c\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2%2821%2F4-9y%2F16%29+%2B+y+%2B+6%28153y%2F640+%2B+807%2F160%29+=+46\"$ ....solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"21%2F2+-+9y%2F8+%2B+y+%2B459y%2F320+%2B+2421%2F80+=+46\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+-+9y%2F8+%2B+y+%2B459y%2F320+=+46-21%2F2-+2421%2F80+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+419y%2F320+=+419%2F80\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+y+=+%28419%2F80%29%28320%2F419%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+y+=+%281%2F1%29%284%2F1%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+y+=+4\"$ \r
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\n" ); document.write( "\n" ); document.write( "go to $\"x+=+21%2F4-9y%2F16\"$ ............eq.1a, substitute $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+21%2F4-%289%2A4%29%2F16\"$
\n" ); document.write( " $\"x+=+21%2F4-9%2F4\"$
\n" ); document.write( " $\"x+=+12%2F4\"$
\n" ); document.write( " $\"x+=+3\"$ \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "go to $\"+z=153y%2F640+%2B+807%2F160\"$ .............eq1c, substitute $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+z=%28153%2A4%29%2F640+%2B+807%2F160\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+z=%28153%2Across%284%29%29%2F%28cross%28640%29160%29+%2B+807%2F160\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+z=153%2F160+%2B+807%2F160\"$
\n" ); document.write( " $\"+z=960%2F160\"$
\n" ); document.write( " $\"+z=6\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so, your solutions are: $\"x+=+3\"$ , $\"y+=+4\"$ , $\"+z+=+6\"$ \r
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