Algebra 101

[mathgrant]

OK class, let's learn some algebra.

a=a
a+b=b+a
a*b=b*a
a*(b+c)=a*b+a*c
If a=b and b=c then a=c
If a=b then b=a
a+0=a
a*1=a
a*0=0

IMPORTANT!
If a=b:
a+c=b+c
a-c=b-c
a*c=b*c
a/c=b/c

Also, if a=b and c=d:
a+c=b+d
a-c=b-d
a*c=b*d
a/c=b/d

Solve all 12 of these equations/equation systems, and you pass.

1. x=0*x+42
2. x*1*1*1=61
3. x+6=8+6
4. 2(x+6)=100+x
5. 6*(3x+8)-7*(2x-11)=149

6. x+y=7+100, x-y=7-100
7. x+2y=10, 2x+y=11
8. 7x=3y-1, x-1=y
9. 931-x=y+x, 911+x=y-x

10. x+y+z=10, x-y=1, z-y=6
11. §+¨=©+ª, §=¨+©+ª, §+¨+©=ª, §=¨+42
12. -9§+6¨+6©-3ª=-105, 2§+10¨-7©-6ª=3, 6§+10¨+10©+2ª=14, -9§+3¨+6©-10ª=-171

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GL DPWestley: I had my backspace key removed and a beverage dispenser pur in it's place. See? I can't go back and fix "put."
GLmathgrant: I once was banned from a M:TG tourney for bringing over 50 banned cards! They were Ace of Clubs, Ace of Diamonds, Ace of Hearts, Ace of Spades, 2 of Clubs. . .

[mikegoo]

I like #6

[CrystyB]

spacing #11 and #12 to a more readable/easy-to-follow form...

code:

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11.  §   + ¨ = © +   ª


     §   = ¨ + © +   ª


     §   + ¨ + © =   ª


         § = ¨ + 42


12. -9§+ 6¨+ 6©- 3ª= -105


     2§+10¨- 7©- 6ª=    3


     6§+10¨+10©+ 2ª=   14


    -9§+ 3¨+ 6©-10ª= -171

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HINT: Using Kramer's way of solving a system of linear equation, we get (105084/17514, 17514/17514, -87570/17514, 157626/17514).

[This message has been edited by CrystyB (edited 01-07-2003 02:53 AM).]