document.write( "Question 186588This question is from textbook saxon algebra 2
\n" ); document.write( ": Solve the system of equations.
\n" ); document.write( "2x+y+z=9
\n" ); document.write( "-2x+3y+z=5
\n" ); document.write( "3x-y+2z=10 \n" ); document.write( "
Algebra.Com's Answer #139910 by uday1435(57)\"\" \"About 
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There are several methods to solve these equations. Matrix method, Cramers rule etc. Since I do not have the book mentioned, I shall solve it directly by manipulating the equations. Let us number these equations as
\n" ); document.write( "2x+y+z=9 (1)
\n" ); document.write( "-2x+3y+z=5 (2)
\n" ); document.write( "3x-y+2z=10 (3)\r
\n" ); document.write( "\n" ); document.write( "Eqn(1) – eqn(2) gives
\n" ); document.write( "4x -2y = 4 let this be eqn(4)\r
\n" ); document.write( "\n" ); document.write( "Multiplying eqn(2) by 2 we get \r
\n" ); document.write( "\n" ); document.write( "4x + 2y + 2z = 18 Now subtract eqn(3) from this
\n" ); document.write( "3x – y + 2z = 10
\n" ); document.write( " x + 3y = 8 let this be eqn (5)\r
\n" ); document.write( "\n" ); document.write( "Now multiply eqn (5) by 4 and subtract eqn (4) from it\r
\n" ); document.write( "\n" ); document.write( "4x + 12 y = 32 That is 4 x Eqn(5)
\n" ); document.write( "4x - 2y = 4 rewrote eqn 4 to subtract
\n" ); document.write( "14 y = 28 after subtraction
\n" ); document.write( "y = 2
\n" ); document.write( " Plug-in the value of y in eqn (5)
\n" ); document.write( "That is x + 3(2) = 8, ie. x + 6 = 8, so x = 2
\n" ); document.write( "Now plug –in these values in eqn (1)
\n" ); document.write( "2(2) + (2) + z = 9
\n" ); document.write( "4+2+z =9; 6+z =9 so z= 9-6 =3. Therefore x = 2, y= 2 and z = 3 are the solutions.
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