解三元一次方程组x 2y-z=3 2x y z=5 3x 4y z=10
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设x=k,y=2k,z=3k2x-y+3z=21===>2k-2k+9k=21解得k=7/3所以x=7/3,y=14/3,z=7x:y=1:2,x:z=1:3,2x-y+3z=212x=y,z=3x,
∵x/7=y/10=z/5∴x=7z/5y=2z又∵x+2y+3z=84∴(7z/5)+2(2z)+3z=84化简可得(7/5)z+7z=84解得z=10∴x=7z/5=(7*10)/5=14y=2z
x=5y/3z=3x/7=5y/710y/3-y-5y/7=3434y/21=34y=21x=35z=15
2x+y=4(1),x+3z=1(2),x+y+z=7(3)由(2)得x=1-3z(4)将(4)代入(1)得2(1-3z)+y=4y=2+6z(5)将(4)(5)代入(3)得(1-3z)+(2+6z)
由前两个式子得y=3-2x,z=3x-7,带入第三个得x-3+2x+3x-7=0,所以x=5/3,y=-1/3,z=-2
用换元法最简单.令x/7=y/10=z/5=t,则x=7t,y=10t,z=5t代入2x+3y-2z=342×7t+3×10t-2×5t=3434t=34t=1x=7t=7y=10t=10z=5t=5
解题过程如下,希望对你有所帮助:
①2x-y=8y=2x-8②3y+z=-73y+z=-73(2x-8)+z=-76x+z=17z=17-6x③4z-x=-74z-x=-74z-x=-74z-x=-74z-x=-74(17-6x)-x
由x:y=2:1得x=2y,代入2x-y=3z,可得3y=3z,z=y于是x+y+z=2y+y+y=20,y=5,x=10,z=5于是x=10,y=5,z=5
x:y=3:2,则x=y*3/2y:z=5:4,则z=y*4/5x+y+z=y*3/2+y+y*4/5=y*(3/2+1+4/5)=y*33/10=6所以y=20/11则x=y*3/2=30/11z=
令a=十分之x=五分之y=七分之z则x=10ay=5az=7a代入3x+2z=4430a+14a=4444a=44a=1所以x=10a=10y=5a=5z=7a=7
3x=3y=6z=>x=y=2z设x=a则y=a,z=2ax+2y+z=16a+2a+2a=165a=16a=16/5x=16/5y=16/5z=32/5
x:y:z=1:2:3x+y+z=36、x=ay=2az=3aa+2a+3a=36a=6x=6y=12z=18
y+2z=-2(1)3x-4z=1(2)2x-y=8(3)(1)+(3)2x+2z=6所以4x+4z=12(4)(2)+(4)7x=13x=13/7y=2x-8=-30/7z=(-y-2)/2=8/7
式②变换一下y=z+3带入式①x-2y=-9得到式④x-2(z+3)=-9,即x-2z=-3,联立式③2z+x=47得到x=22,z=12.5,y=15.5
x+y+z=6(1)y-z=4(2)x-y-2z=3(3)(1)-(3)=2y+3z=3y-z=42y-2z=8联立得z=-1,y=3,x=4
x+2y=2(1)2y+3z=4(2)x+3z=6(3)(1)+(2)+(3)2x+4y+6z=12x+2y+3z=6(4)(4)-(1)得3z=4z=4/3(4)-(2)得x=2(4)-(3)得2y
x+y+z=22(1)3x+y=47(2)x-4z=2(3)由(2),(3)得y=47-3xz=(x-2)/4代入(1)x+47-3x+(x-2)/4=22-8x+188+x-2=887x=98所以x
由x:y:z=1:2:3可得y=2x,z=3x代入x+y+z=36得6x=36于是x=6,y=12,z=18
3x-y=-7①y+4z=3③2x-2z=-5③①加③3x+4z=-4④3③-2④z=1/2代入①和③x=-2y=1