a) ⎩⎨⎧x+y+z=10 ∣−y−zx+y−z=20x−y−z=30
⎩⎨⎧x=10−y−zx+y−z=20x−y−z=30
⎩⎨⎧x=10−y−z10−y−z+y−z=2010−y−z−y−z=30
{10−y−z+y−z=2010−y−z−y−z=30
{10−2z=20 ∣−1010−2y−2z=30 ∣−10
{−2z=10 ∣:(−2)−2y−2z=20 ∣:2
{z=−5−2y−2⋅(−5)=20 {z=−5−2y−2⋅(−5)=20
{z=−5−2y+10=20 ∣−10
{z=−5−2y=10 ∣:(−2)
{z=−5y=−5
⎩⎨⎧x+y+z=10z=−5y=−5
⎩⎨⎧x+(−5)+(−5)=10z=−5y=−5
⎩⎨⎧x−10=10 ∣+10z=−5y=−5
⎩⎨⎧x=20z=−5y=−5
b) ⎩⎨⎧3x+2y+z=7 ∣−3x−2yx+2y+3z=15x−3y−z=8
⎩⎨⎧z=7−3x−2yx+2y+3z=15x−3y−z=8
⎩⎨⎧z=7−3x−2yx+2y+3(7−3x−2y)=15x−3y−(7−3x−2y)=8
{x+2y+3(7−3x−2y)=15x−3y−(7−3x−2y)=8
{x+2y+21−9x−6y=1 ∣−215x−3y−(7−3x−2y)=8
{−8x−4y=1−215x−3y−7+3x+2y=8
{−8x−4y=−208x−y−7=8 ∣+7
+ {−8x−4y=−208x−y=15
−8x+8x−4y−y=−20+15
−5y=−5 ∣:(−5)
y=1
{y=18x−y=15
{y=18x−1=15 ∣+1
{y=18x=16 ∣:8
{y=1x=2
⎩⎨⎧3x+2y+z=7y=1x=2
⎩⎨⎧3⋅2+2⋅1+z=7y=1x=2
⎩⎨⎧6+2+z=7y=1x=2
⎩⎨⎧8+z=7 ∣−8y=1x=2
⎩⎨⎧z=−1y=1x=2
