(Solved): 2. Find a general form for ALL the solutions of the LDE below. Otherwise, explain why no solutions ...

2. Find a general form for ALL the solutions of the LDE below. Otherwise, explain why no solutions are possible. a) $21x+14y=147$ b) $4x?6y=77$ 3. A wallet contains \$5-bills and \$10-bills amounting to \$45.00. How many of each kind could there be in all? Use the LDE method discussed in class to solve this problem. 4. Use the properties of modulo to determine the unit digit of the standard form of $3^{407}$. 5. Use properties of modulo to determine the remainder when $2^{1000}$ is divided by 7 . 6. Prove: If $a=b(\mathrm{modm})$ and $c=d(\mathrm{modm})$, then $ac=bd(\mathrm{modm})$.