如果方程组3x y=2k﹢3 x﹢3y=5
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![如果方程组3x y=2k﹢3 x﹢3y=5](/uploads/image/f/3698127-63-7.jpg?t=%E5%A6%82%E6%9E%9C%E6%96%B9%E7%A8%8B%E7%BB%843x+y%3D2k%EF%B9%A23+x%EF%B9%A23y%3D5)
解题思路:解关于x,y的方程组,用k表示出x,y,再列不等式求出k解题过程:解:
x+y=5k(1)x-y=9k(2)(1)+(2)2x=14kx=7k(1)-(2)2y=-4ky=-2k把x=7k,y=-2k代入2x+3y=6得14k-6k=68k=6k=3/4
2X=3Y①和3X+4Y=2K+1,②满足方程X+Y=3,③由①,③解得x=9/5,y=6/5,代入②,2k+1=51/5,k=23/5.
3x+y=-4k+1x+3y=3把k作为参数,解方程组得到:x=-3k/2y=1+k/2将解带入不等式,则:2x+y>2=>-3k+1+k/2>2=>-5k/2>1=>k
由题意得,X=﹣Y①把①代入2x+3y=2k+1得,Y=2K+1②把①代入3X-2Y=4K+3得,﹣5Y=4K+3即Y=﹣4K+3/5③有②③可以得到2K+1=-4K+3/5即10K+5=﹣4K-3解
3x+5y=k+1,2x+3y=k,这个方程整理一下3x+5y-1=k所以3x+5y-1=2x+3y整理得x+2y=1x+y=2,解这个新方程组x=3,y=-1代入2x+3y=k,中,k=3
解出x=(7k-4)/5y=(-8k+11)/5由x>yk>1
x+2y=k+1(1)3x-y=k-1(2)(1)+(2)×27x=3k-1x=(3k-1)/7
将4x+3y=k代入3x-2y=5k中,得:x+y=0,在于2x+3y=6联立,解得x=-6,y=6
3x+y=k①x+3y=2②②乘以3,得3x+9y=6③③减去①,得8y=6-ky=(6-k)/8将y=(6-k)/8代入②中,得x+3(6-k)/8=2x=2-3(6-k)/8因为x,y
2x+y=3k-1(1)x+2y=-2(2)由(1)*2-(2)得3x=6k-2+2x=2k代入(1)得y=3k-1-4k=-k-1由于x>3y≤-3,则2k>3-k-1≤-3k>3/2k≥2∴k≥2
2x+y=3k+1x+2y=3-2k相加3x+3y=4+kx+y=5则3x+3y=15所以4+k=15k=11
x=y代入3x+5y=3x+5x=8x=k-4x=(k-4)/82x+3y=2x+3x=5x=kx=k/5所(k-4)/8=k/55k-20=8kk=-20/3
两个方程相加,得到5x+5y=2k+2x=y=12,5x+5y=60所以2k+2=60k=29
由①-②,得x-y-(x+3y)=2k-(3k-1)x-y-x-3y=2k-3k+1-4y=-k+1y=(k-1)/4由①×3+②,得3x-3y+x+3y=6k+3k-14x=9k-1x=(9k-1)
(1)k=5/8①*5-②得12k=-4k+10k=5/10(2)a=-12ax+4y=1212x-4y=4(12+a)x=16当a=-12时方程无实数解(3)3x+5y=m+2①2x+3y=m②②*
4x-3y=7,[(k+1)/2]x-y=k-3.8x-6y=14,3(k+1)x-6y=6k-18.二式减一式等于:(3k-5)x=6k-32,x=(6k-32)/(3k-5)有得:y=(3k-27
因为方程组(2K-1)X-(K+1)Y=3K和(4K-1)X-(3K+1)Y=5K+4.所以(4K-1)(2K-1)X-(4K-1)(K+1)Y=3K(4K-1)和(2K-1)(4K-1)X-(2K-
4x-3y=k①2x+3y=5②①-②×2得:4x-3y-4x-6y=k-10-9y=k-10y=-(k-10)/9①+②得:4x-3y+2x+3y=k+56x=k+5x=(k+5)/6因为x