document.write( "Question 1176506: Solve the system of equations. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, enter INFINITELY MANY.)\r
\n" ); document.write( "\n" ); document.write( "x + y − 7z = −1
\n" ); document.write( "y − z = 0
\n" ); document.write( "−x + 6y = 1
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Algebra.Com's Answer #803582 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Second equation says  y = z.\r\n" );
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document.write( "Using it, replace z in the first equation by y.  \r\n" );
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document.write( "You will get the first equation in the form\r\n" );
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document.write( "    x + y - 7y = -1,   or\r\n" );
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document.write( "    x - 6y = -1.\r\n" );
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document.write( "It is the same as (or equivalent to) the third equation.\r\n" );
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document.write( "It means that the system has infinitely many solutions.\r\n" );
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document.write( "We can take z as a free variable, to which we can give any value.\r\n" );
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document.write( "Then  y = z  and  x = (from the very first equation)  -1 - y + 7z = -1 - z + 7z = -1 + 6z.\r\n" );
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document.write( "Thus the general formulas for the infinite numbers of solutions is\r\n" );
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document.write( "    (x,y,z) = (-1+6z, z, z).      \r\n" );
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document.write( "ANSWER.  There are infinitely many solutions.\r\n" );
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document.write( "         The general formula for the solutions is  (x,y,z) = (-1+6z,z,z).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved and explained.\r
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