How many solutions are there for |x-1|-y=-5 and |x-1|+

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How many solutions are there for |x-1|-y=-5 and |x-1|+ [#permalink]

06 Dec 2003, 14:51

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1.How many solutions are there for |x-1|-y=-5 and |x-1|+ |y-5|=1

a.0
b.1
c.2
d 3
e. 4

Last edited by Praetorian on 08 Dec 2003, 00:57, edited 1 time in total.

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[#permalink]

06 Dec 2003, 16:12

Praet--

That's a fantastic question. I tried to simplify and I just got a bee's nest. I ha ve no idea. I wonder if I missed something obvious.

-5(|x-1| + |y-5|)= |x-1|-y
-5|x-1| -5|y-5|= |x-1|-y
-6|x-1| -5|y-5|=-y
-6|x-1| =5|y-5|-y

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Re: PS : Modulus [#permalink]

07 Dec 2003, 06:05

praetorian123 wrote:

1.How many solutions are there for |x-1|-y=-5 and |x-1|+ |y-5|=1

a.0
b.1
c.2
d 3
e. 4

This is a good problem:

IMO, the answer is c.
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Re: PS : Modulus [#permalink]

07 Dec 2003, 06:28

praetorian123 wrote:

1.How many solutions are there for |x-1|-y=-5 and |x-1|+ |y-5|=1

a.0
b.1
c.2
d 3
e. 4

heres what i get .
|x-1|-y=-5 ........(1)

2. |x-1|+ |y-5|=1 .....(2)

from (1) , |x-1|= y-5
Substitute in equation (2).
y-5 + |y-5| = 1
|y-5| = 6 - y

therefore,
y-5 = - (6-y) , which gives no solution
y -5 = 6- y , which gives ... y = 11/2

Substitute back in (1)

|x-1|-y=-5

|x-1|= y-5

x-1 = - y+5

i. x = -y + 6

= -11/2 + 6

= 1/5

ii. x-1 = y-5

x = y -4

= 11/2 - 4

x = 3/2

in other words, we have two solutions.

1. x = 1/5 , y= 11/2
2. x= 3/2 , y=11/2

did i do this right?

thanks
praetorian

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Re: PS : Modulus [#permalink]

09 Dec 2003, 05:13

praetorian123 wrote:

is my solution ok?

That is essentially how I solved it, but I didn't take ALL of the steps. Remember, we only needed to know how many solutions there were, not what the solutions actually are!
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Re: PS : Modulus [#permalink] 09 Dec 2003, 05:13

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How many solutions are there for |x-1|-y=-5 and |x-1|+

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How many solutions are there for |x-1|-y=-5 and |x-1|+

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