11x-10y=1011base two
10x+11y=1001base two
To solve the system of equations, we can first rewrite them in base 10 form.
The first equation, 11x - 10y = 1011 base two, can be rewritten as:
3x - 2y = 11 base 10
The second equation, 10x + 11y = 1001 base two, can be rewritten as:
2x + 3y = 9 base 10
Now we have a system of two equations in base 10 form:
3x - 2y = 11
2x + 3y = 9
To solve this system, we can use the elimination method.
Multiply the first equation by 3 and the second equation by 2 to eliminate the y variable:
9x - 6y = 33
4x + 6y = 18
Add the two equations:
(9x - 6y) + (4x + 6y) = 33 + 18
13x = 51
x = 51 / 13
x = 3
Substitute the value of x into one of the original equations, let's use the first equation:
3x - 2y = 11
3(3) - 2y = 11
9 - 2y = 11
-2y = 11 - 9
-2y = 2
y = 2 / -2
y = -1
Therefore, the solution to the system of equations is x = 3 and y = -1.