Number and algebra question

1.(a) 2x + 3y - 1 = 0...[1]
3x+5y - 1 = 0...[2]
From [1]
2x+3y-1=0
2x+3y=1...[3]
[3]*3
6x+9y=3...[5]
From[2]
3x+5y-1=0
3x+5y=1...[4]
[4]*2
6x+10y=2...[6]
[5]-[6]
6x+9y=3
-) 6x+10y=2
-y=1
y=-1
Sub. y=-1 into [3]
2x+3(-1)=1
2x-3=1
2x=4
x=2
So x=2,y=-1


(b) 2/a+3/b = 1
3/a + 5/b = 1
Let x=1/a,y=1/b
By(a).1/a=x=2 and so a=0.5
1/b=y=-1 and so b=-1
So a=0.5, y=-1


2.It is difficult to use word to explain what is grahical method.
(I will tell you later)



3. Yes, you need, but your answer(i.e. Ans.a=0.5,b=-0.5) is likely wrong.
The correct answer is a=2,b=1

2013-02-02 13:10:28 補充：
2. You can turn from 8.7to 8.11. There are many examples.

1(a) 2x+3y-1=0....(1)
3x+5y-1=0....(2)
5(1)-3(2): x=-2=0. x=2
Putting x=2 into (1): 2(2)+3y-1=0, y=-1

1(b) Rewrite the equations into
2/(1/a)+3(1/b)-1=0 and 3(1/a)+5(1/b)-1=0.
Using part (a), 1/a=2 and 1/b=-1,
a=1/2 and b=-1

2.
In general, the equation Ax+By+C=0 has manysolutions (x,y).
Each solution (x,y) can be representedgraphically by a point in the coordinate plane.
All the solutions of Ax+By+C=0 form a straight line.

Solving simultaneous equations Ax+By+C=0 and ax+by+c=0 means to find the common solution(s) of both equations. Thecommon solution(s) are the point(s) of intersection of the two linesrepresenting the two equations.

If we solve the simultaneous equations by first drawing the graph of each equation and then finding the point(s) of intersection, it is known as graphical method.
3.
Writing the answer again at the end of the solution looks neat and tidy but not necessary.