Question

11x+10y=10001
10x-y=10
Leave your answer in base 2

Answer 1

To solve this system of equations, let's multiply the second equation by 10 and add it to the first equation:

11x + 10y = 10001
10(10x - y) = 10(10)
100x - 10y = 100

Now we have the following equation:

111x = 10101

To find x, we divide both sides by 111:

x = 10101 / 111

Now let's convert x to base 2:

10101 (base 10) = 10000011110101 (base 2)

So, x = 10000011110101 (base 2).

To find y, we substitute the value of x back into the second equation:

10x - y = 10
10(10000011110101) - y = 10
100000111101010 - y = 10
- y = 10 - 100000111101010
y = 100000111101010 - 10
y = 100000111100000

So, y = 100000111100000 (base 2).

Therefore, the solution to the system of equations in base 2 is x = 10000011110101 and y = 100000111100000.