吧方程组x² y²=5,x²-5xy 6y²化成另两个二元二次方程组

1,x+y/2+x-y/3=6即：5x-y=36①4(x+y)-5(x-y)=2即:-x+9y=2②①+②*5==可接2,先化整：3（x+y）+2（x-y）=36①4(x+y)-5(x-y)=2②①*

设（x+y）为t,(x-y)为p,所求的解为c所以t/2+p/2=64t-5p=c整理得：5t+5p=604t-5p=c两式相加得9t=60+cc=9t-60所以4(x+y)-5(x-y)=9(x+y

5x+y=369y-x=2即45y-10+y=36y=1x=7

补充题目：已知方程组5x+y=3;ax+5y=4与方程组x-2y=5,5x+by=4有相同的解,求a,b的值.解答；说明,最后相同的解是四个方程的解也为方程组5x+y=3,x-2y=5的解此方程组的解

｛5（x＋y）＋3（x－y）＝2｛7（x＋y）－3（x－y）＝－6原方程组化简得﹛4x+y=1(1)2x+5y=-3(2)(1)×5得20x+5y=5(3)(3)-(2)得18x=8x=4/9代入（1

2/(x+y)+5/(x-y)=189/(x+y)-10/(y-x)=66设x+y=a,x-y=b,原方程化为2/a+5/b=18-----1(1)9/a+10/b=66-------(2)(2)-(

另a=1/（x+y）,b=1/(x-y);则2a+5b=18；9a+10b=66；解得a=6,b=6/5；即       &nbs

(x+y)/2+(x-y)/3=6①5(x+y)-2(x-y)=4②由①得3x+3y+2x-2y=365x+y=36y=36-5x③由②得5x+5y-2x+2y=43x+7y=4④③代入④得3x+25

5(x+y)+3(x-y)=908x+2y=901式5(x+y)-3(x-y)=302x+8y=302式1式乘以4-2式解得x=11y=1

x=66/37y=-28/37

设a=x+y,b=x-y原方程组为：a/2+b/3=6,即3a+2b=36,即：12a+8b=1444a-5b=12,即：12a-15b=36相减得：23b=108,得：b=108/23,再得：a=1

方程化为－x+7y=1117x+3y=272将1式化为x=7y-113则将3式代入2式可得7（7y-11）+3y=2752y=104y=2x=7×2-11x=3所以解得x＝3y＝2

{(x-2)(y+3)=(x+1)(y-1){(x+1)(y+1)=(x-1)(y+5){xy+3x-2y-6=xy-x+y-1{xy+x+y+1=xy+5x-y-5{4x-3y=5(1){4x-2y

3x=4(x-y)化简得x-y=0…………①x-8(x-y)=58y-7x=5…………②①×7+②得15x=5x=3分之1把x=3分之1代入①得3分之1-y=0y=3分之1∴x=3分之1,y=3分之1

令x/4=y/5=K,则x=4k,y=5k.所以12k-10k=10.解得K=5.则x=4k=20,y=5k=25.所以x=20,y=25

x=-11,y=-19|2

x+y=a(1)(a-1)x+y=5(2)(2)-(1)(a-1-1)x=5-ax=(5-a)/(a-2)y=a-x=a-(5-a)/(a-2)=(a²-a-5)/(a-2)

展开x^2-2y^2-xy=-5x^2-2y^2+xy=7所以x^2-2y^2=1xy=6上式除以下式,解分式方程x/y=3/2或-4/3(舍去)所以x^2=9y^2=4x=3y=2或x=-3y=-2

设1/x+y=t1/x-y=v则3t+2v=17/52t-5v=16t+4v=34/56t-15v=319v=19/5v=1/5t=11/x+y=11/x-y=1/5x+y=1x-y=5x=3y=-2