document.write( "Question 369070: I am needing help with a system of equations with 3 variables
\n" ); document.write( "The first equation in this problem is 6q-r+2s=8
\n" ); document.write( "The second equation is 2q+3r-s=-9
\n" ); document.write( "The third equation is 4q+2r+5s= 11
\n" ); document.write( "I am in Algebra 2 in high school and know how to use substitution and elimination. \n" ); document.write( "

Algebra.Com's Answer #263001 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
1. $\"6q-r%2B2s=8\"$
\n" ); document.write( "2. $\"2q%2B3r-s=-9\"$
\n" ); document.write( "3. $\"4q%2B2r%2B5s=+11\"$
\n" ); document.write( "You use elimination to reduce from 3 equations to 2 equations.
\n" ); document.write( "Multiply eq. 2 by 2 and add to eq. 1,
\n" ); document.write( " $\"6q-r%2B2s%2B4q%2B6r-2s=8-18\"$
\n" ); document.write( " $\"10q%2B5r=-10\"$
\n" ); document.write( "4. $\"2q%2Br=-2\"$
\n" ); document.write( "Multiply eq. 2 by 5 and add to eq. 3,
\n" ); document.write( " $\"4q%2B2r%2B5s%2B10q%2B15r-5s=11-45\"$
\n" ); document.write( "5. $\"14q%2B17r=-34\"$
\n" ); document.write( "Multiply eq. 4 by -7 and add to eq. 5,
\n" ); document.write( " $\"14q%2B17r-14q-7r=-34%2B14\"$
\n" ); document.write( " $\"10r=-20\"$
\n" ); document.write( " $\"highlight%28r=-2%29\"$
\n" ); document.write( "Then work backwards and substitute,
\n" ); document.write( "From eq. 4,
\n" ); document.write( " $\"2q-2=-2\"$
\n" ); document.write( " $\"highlight%28q=0%29\"$
\n" ); document.write( "From eq. 1,
\n" ); document.write( " $\"6%280%29-%28-2%29%2B2s=8\"$
\n" ); document.write( " $\"2s=6\"$
\n" ); document.write( " $\"highlight%28s=3%29\"$ \n" ); document.write( "

\n" );