Question 369070
1.{{{6q-r+2s=8}}}
2.{{{2q+3r-s=-9}}}
3.{{{4q+2r+5s= 11}}}
You use elimination to reduce from 3 equations to 2 equations.
Multiply eq. 2 by 2 and add to eq. 1,
{{{6q-r+2s+4q+6r-2s=8-18}}}
{{{10q+5r=-10}}}
4.{{{2q+r=-2}}}
Multiply eq. 2 by 5 and add to eq. 3,
{{{4q+2r+5s+10q+15r-5s=11-45}}}
5.{{{14q+17r=-34}}}
Multiply eq. 4 by -7 and add to eq. 5,
{{{14q+17r-14q-7r=-34+14}}}
{{{10r=-20}}}
{{{highlight(r=-2)}}}
Then work backwards and substitute,
From eq. 4,
{{{2q-2=-2}}}
{{{highlight(q=0)}}}
From eq. 1,
{{{6(0)-(-2)+2s=8}}}
{{{2s=6}}}
{{{highlight(s=3)}}}