數條數學問題..(20分)

1)
3x+5y = 7---(1)
5x-3y=6---(2)
From (1)
y=(7-3x)/5---(3)
Sub (3) into (2)
5x-3(7-3x)/5=6
25x-3(7-3x)=30
25x-21+9x=30
34x=51
x=51/34=3/2

when x=3/2
y=(7-3x3/2)/5
y=(7-4.5)/5
y=2.5/5
y=0.5

2)
11x+2y=4(x+y)---(1)
10(x-y)=x-y-45---(2)

From (1)
11x+2y=4x+4y
11x-4x=4y-2y
7x=2y----(3)

From (2)
10(x-y)=x-y-45
10x-10y=x-y-45
10x-x-10y+y=-45
9x-9y=-45
x-y=-5
x=y-5----(4)

Sub (4) into (3)
7(y-5)=2y
7y-35=2y
5y=35
y=7

So x=7-5=2



3)6(a-1)^2 + 2a(a-1)
=(a-1)[6(a-1)+2a]<----common factor=a-1
=(a-1)(6a-6+2a)
=2(a-1)(3a-3+a)<---common factor=2
=2(a-1)(4a-3)

4)

2y^2-200
=2(y^2-100)<----common factor=2
=2(y+10)(y-10)<----Use (a+b)(a-b)=a^2-b^2

5) a^2-b^2-a-b
=(a+b)(a-b)-(a+b)
=(a+b)(a-b-1)

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