\left \{ {{5x+3y=0} \atop {-x-2y=7}} \right. drugie równanie *5
\left \{ {{5x+3y=0} \atop {-5x-10y=35}}
… dodajemy stronami
-7x=35
x=-5 podstawiamy do pierwszego lub drugiego równania
5x+3*(-5)=0
5x-15=0
5x=15
x=3
\left \{ {{x=3} \atop {y=-5}}
…
\left \{ {{3u+2v=2}/*(-2) \atop {5u+4v=6}}
\left \{ {{-6u-4v=-4} \atop {5u+4v=6}}
…
-u=2
u=-2
3*(-2)+2v=2
-6+2v=2
2v=2+6
2v=8
v=4
\left \{ {{u=-2} \atop {v=4}}
…
\left \{ {{3s+5t=-6} \atop {1,5s-2t=-3}} /*(-2)
\left \{ {{3s+5t=-6} \atop {-3s+4t=6}}
…
9t=0
t=0
3s+5t=-6
3s=-6
s=-2
\left \{ {{s=-2} \atop {t=0}}
…
\left \{ {{5=3x-y} \atop {5x-2y=5}}
\left \{ {{3x-y=5}/*(-2) \atop {5x-2y=5}}
\left \{ {{-6x+2y=-10}\atop {5x-2y=5}}
…
-x=-5
x=5
3*5-y=5
15-y=5
-y=5-15
-y=-10
y=10
\left \{ {{x=5} \atop {y=10}}
…
\left \{ {{x-3y=5} \atop {y+3x=-5}}
\left \{ {{x-3y=5}\*(-3) \atop {3x+y=-5}}
\left \{ {{-3x+9y=-15} \atop {3x+y=-5}}
…
10y=-20
y=-2
x-3*(-2)=5
x+6=5
x=5-6
x=-1
\left \{ {{x=-1} \atop {y=-2}}