31basex+20basey=23base10
23basex_11basey=5base10
3x+1 + 2y = 23
2x+3 - (y+1) = 5
Now solve for x and y as usual
To solve these equations, we need to convert the numbers to base 10 first. Let's start with the first equation:
31basex + 20basey = 23base10
To convert base x to base 10, we multiply each digit by the corresponding power of x and then sum them up. So, in base 10, the equation becomes:
3x^1 + 1x^0 + 2y^1 + 0y^0 = 2x^1 + 3x^0
Simplifying this equation, we get:
3x + 1 + 2y = 2x + 3
Next, let's work on the second equation:
23basex_11basey = 5base10
To convert base x_11 and base y to base 10, we use the same process as before:
2(x_11)^1 + 3(x_11)^0 + 1(y)^1 + 1(y)^0 = 5
Simplifying this equation yields:
2(x_11) + 3 + y + 1 = 5
Combining like terms, we have:
2(x_11) + y = 1
Now we have the system of equations:
3x + 1 + 2y = 2x + 3
2(x_11) + y = 1
At this point, we can't solve the system of equations directly because we have two unknowns, x and y, and a different base x_11. We need more information to continue.