1) For what value of the constant *a* does the system of equations below have infinitely many solutions?

\( \begin{align*} 3x + 2y &= 8,\\ 6x &= 2a - 7 - 4y \end{align*}\)

I tried over and over again and don't seem to get the right answer. I got 23/6(or sothing like that) for the first time and now 37/6 ...

2) How many numbers between 1 and 2005 are integer multiples of 3 or 4 but not 12?

What trick can I use to solve this quickly?

3) Using the letters X and Y, the following two-letter code words can be formed: XX, XY, YY, YX. Using the letters X, Y, and Z, how many different 3 letter code words can be formed?

Same here...

Thanks in advance!!! i would prefer you answer 1) first.

Guest Sep 5, 2018

#1**+1 **

1) Try a = 23/2. With this value, equation 1 multiplied by 2 is exactly the same as equation 2.

2) Try dividing 2005/3 + 2005/4 - 2005/6. Ignore the fractional parts.

3) If you are allowed to repeat the letters, then you should have: 3^3 = 27

Guest Sep 5, 2018

edited by
Guest
Sep 5, 2018

edited by Guest Sep 5, 2018

edited by Guest Sep 5, 2018