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February 8th, 2015, 02:43 PM   #1
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System of Equations

Hello, my name is Gabriel and I'm from Brazil. This was one of the questions of my entrance test this year, which I take so I can attend a university, just like the SAT in the US. My math teacher couldn't solve it, neither could I. I used the TI-nspire CX CAS calculator to find the asnwer. May you try to solve it, please? Thank you!


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February 8th, 2015, 03:10 PM   #2
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add 1st & 3rd equations ...

$\displaystyle |2x-1| + \left|x - \frac{1}{2} \right| + 2^{y+1} = 11$

multiply by 2 ...

$\displaystyle 2|2x-1| + |2x - 1| + 2^{y+2} = 22$

$\displaystyle 3|2x-1|+ 2^{y+2} = 22$

subtract the 2nd equation ...

$\displaystyle 2^{y+1} = 8$

$\displaystyle y = 2$

substitute $\displaystyle y = 2$ into the 2nd equation ...

$\displaystyle 3|2x-1| + 8 = 14$

$\displaystyle x = \frac{3}{2} ; x = -\frac{1}{2}$

you should be able to determine z from this point ...
Thanks from gabemreis
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February 8th, 2015, 03:26 PM   #3
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It looks so simple now! Haha. Thank you very much
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