document.write( "Question 502971: Please help me solve this.
\n" ); document.write( "Is this system dependent or independent?\r
\n" ); document.write( "\n" ); document.write( "x + 2y + z = 4
\n" ); document.write( "3x - 4y + z = 4
\n" ); document.write( "6x - 8y + 2z = 8 \n" ); document.write( "
Algebra.Com's Answer #339027 by jrb1965(16)\"\" \"About 
You can put this solution on YOUR website!
You have 3 unknowns, but since the second and third equations are the same information (equation 3 is just equation 2 multiplied by 2) you will not have a unique solution so the system will be dependent.\r
\n" ); document.write( "\n" ); document.write( "3x - 4y +z = 4
\n" ); document.write( "x + 2y + z = 4
\n" ); document.write( "_______________ Subtracting equation 1 from equation 2\r
\n" ); document.write( "\n" ); document.write( "2x - 6y = 0, so x = 3y\r
\n" ); document.write( "\n" ); document.write( "Substituting this into equation 3\r
\n" ); document.write( "\n" ); document.write( "18y - 8y + 2z = 8\r
\n" ); document.write( "\n" ); document.write( "10y + 2z = 8, so y = 0.8 - 0.2z, and x = 3y = 2.4 - 0.6z\r
\n" ); document.write( "\n" ); document.write( "Substitute the x and y in terms of z into any of the equations will result in an identity equation\r
\n" ); document.write( "\n" ); document.write( "(2.4 - 0.6z) + 2(0.8 - 0.2z) + z = 4 (substituted into equation 1)\r
\n" ); document.write( "\n" ); document.write( "(2.4 - 0.6z) + (1.6 - 0.4z) + z = 4\r
\n" ); document.write( "\n" ); document.write( "4 = 4, true for all values of z\r
\n" ); document.write( "\n" ); document.write( "So this is a dependent system\r
\n" ); document.write( "\n" ); document.write( "x = 2.4 - 0.6z
\n" ); document.write( "y = 0.8 - 0.2z
\n" ); document.write( "for any chosen value of z\r
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