5到奥数题（好的加分）

1.a(x-3)+b(3x+1)=5(x+1)，
ax-3a+3bx+b=5x+5
(a+3b-5)x=5+3a-b
x有无穷多个解: a+3b-5=0, 5+3a-b=0; 则a=-1, b=2.

2.若关于x、y的方程组{ax+3y=9 2x-y=1 无解，则a的值为（ A. -6）
2x-y=1; y=2x-1;
ax+3(2x-1)=9
(a+6)x = 12, a=-6时无解。

3.若4x-3y-6z=0,x+2y-7z=0(xyz不等于0），
7z = x+2y
6z= 4x-3y
z=-3x+5y
7(-3x+5y) = x+2y
y=(2/3)x; z=(1/3)x
5x^2+2y^2-z^2 = 5x^2 + (8/9)x^2 - (1/9)x^2 = (52/9)x^2
2x^2-3y^2-10z^2 = 2x^2 - (12/9)x^2 - (10/9)x^2 = -(4/9)x^2
5x^2+2y^2-z^2/1x^2-3y^2-10z^2的值等于=(52/9)/(-4/9) = -13; 选D。

4。题目有误：abc, 没有xyz
ab/(a+b) = 1/3; b= a/(3a-1)
bc/(b+c) = 1/4; c= b/(4b-1) = {a/(3a-1)}/{4a/(3a-1) -1} = a/(a+1);
ac/(a+c) = 1/5; c= a/(5a-1)
则 a/(a+1) = a/(5a-1); a= 1/2;
b = 1; c = 1/3.
代入计算即可。

5.
2x-3y+4m=11 (1)
3x+2y+5m=21 (2)
(1)*2 + (2)*3 : 13x + 23m = 85; x= (85-23m)/13;
(2)*2 - (1)*3 : 13y - 2m = 9; y= (9+2m)/13;
代入x, y:
x+3y+7m=20
(85-