1.
3x+5y = 15 …①
2x-3y = -4 …②
①×3+②×5,得(3×3+2×5)x = 15×3+（-4)×5
19x = 25
x = 25/19
代入①有,3×25/19 + 5y = 15
y = (15-75/19)/5 = 3 - 15/19 = 42/19
于是x=25/19,y=42/19.
2.
x/3 + y/4 =1 …①
2x-3y = 5 …②
①×12＋②,有（4+2）x = 17 于是x=17/6
代入②,有2×17/6-3y = 5
y = (17/3 - 5)/3 = 2/9
于是x=17/6,y=2/9
3.
x-2y-3 = 0 ...①
5x+4y+8 = 0 ...②
①×2+②,得7x+2=0,于是x=-2/7
代入①,有y=(x-3)/2 = (-2/7-3)/2 = -23/14
于是x=-2/7,y=-23/14.
4.
x-2y+3z = 0 .①
3x+2y+5z = 12 ..②
2x-4y-z = -7 ...③
①+②得,4x+8z = 12 ...④
②×2+③得,8x+9z = 17 ...⑤
④×2-⑤得,7z = 7,z=1
代入④,有x = (12-8z)/4 = 3-2z = 1
再把z=1,x=1代入①得
y=(x+3z)/2 = 2
于是x=1,y=2,z=1.
5.
2x-3y+4z=12 ...①
x-y+3z=4 ...②
4x+y-3z=-2 ...③
①-②×3,得-x-5z=0 ...④
②+③,得5x=2 x=2/5
代入④,有 z = -1/5·x = -2/25
將x=2/5,z=-2/25代入②,有
y=x+3z-4 = 2/5 + 6/25 -4 = -84/25
于是 x=2/5,y=-84/25,z=-2/25.
6.
x+2y+3z=15 ...①
x/3+4z=3 ...②
y/4-3z=3 ...③
①-③×8,得x+27z = -9 ...④
④-②×3,得15z = -18 ,z=-6/5
代入④,有x=-9-27z = 117/5
將z=-6/5代入③,有
y = 4(3+3z) = -12/5
于是x=117/5 ,y=-12/5,z=-6/5.