document.write( "Question 385955: Good Morning:
\n" ); document.write( "I am still working with back substitution to solve the system of linear equations. Can you help me? \r
\n" ); document.write( "\n" ); document.write( "{3/4x+2y+2/3z=-3
\n" ); document.write( "{-4/5y-4/3z=1
\n" ); document.write( "{z=3\r
\n" ); document.write( "\n" ); document.write( "Thanks so much! \r
\n" ); document.write( "\n" ); document.write( "Denise \n" ); document.write( "

Algebra.Com's Answer #273058 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"3%2F4\"$ x + 2y + $\"2%2F3\"$ z = -3
\n" ); document.write( " $\"-4%2F5\"$ y - $\"4%2F3\"$ z = 1
\n" ); document.write( "z = 3
\n" ); document.write( ":
\n" ); document.write( "Replace z with 3 in the 1st two equations
\n" ); document.write( " $\"3%2F4\"$ x + 2y + $\"2%2F3\"$ (3) = -3
\n" ); document.write( " $\"-4%2F5\"$ y - $\"4%2F3\"$ (3) = 1
\n" ); document.write( "Fortunately, this will cause two of fractions to cancel out
\n" ); document.write( " $\"3%2F4\"$ x + 2y + 2 = -3
\n" ); document.write( " $\"-4%2F5\"$ y - 4 = 1
\n" ); document.write( ":
\n" ); document.write( " $\"3%2F4\"$ x + 2y = -3 -2
\n" ); document.write( " $\"-4%2F5\"$ y = 1 + 4
\n" ); document.write( ":
\n" ); document.write( " $\"3%2F4\"$ x + 2y = -5
\n" ); document.write( " $\"-4%2F5\"$ y = +5
\n" ); document.write( ":
\n" ); document.write( "Multiply the above equation by -5, get rid of the denominator change the signs, results:
\n" ); document.write( "4y = -5(5)
\n" ); document.write( "y = $\"%28-25%29%2F4\"$
\n" ); document.write( "y = -6.25
\n" ); document.write( ":
\n" ); document.write( "Find x, substitute for y and z
\n" ); document.write( " $\"3%2F4\"$ x + 2y + $\"2%2F3\"$ z = -3
\n" ); document.write( "y=-6.25, z=3
\n" ); document.write( " $\"3%2F4\"$ x + 2(-6.25) + $\"2%2F3\"$ (3) = -3
\n" ); document.write( " $\"3%2F4\"$ x -12.5 + 2 = -3
\n" ); document.write( " $\"3%2F4\"$ x -10.5 = - 3
\n" ); document.write( " $\"3%2F4\"$ x = -3 + 10.5
\n" ); document.write( " $\"3%2F4\"$ x = 7.5
\n" ); document.write( "Multiply by 4
\n" ); document.write( "3x = 4(7.5)
\n" ); document.write( "3x = 30
\n" ); document.write( "x = 10
\n" ); document.write( ":
\n" ); document.write( "Summarize: x=10; y=-6.25, z=3\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );