Question

Solve the simultaneous equation 11 base x +10 base y = 5 base 10 and 13 base x + 7 base y = 19 base 10

Answer 1

converting to base 10
11 base x +10 base y = 5 base 10 ---> x+1 + y+0 = 5
x + y = 5

13 base x + 7 base y = 19 base 10 ---> x+3 + 7 = 19
x = 9

then in x+y=5 , we would have y = -4

Usually we would expect the "bases" to be whole numbers, but ....

check:
13_x + 7_y = 19₁₀
and if x = 9 and y = -4
1(9)+3 + 7 = 19 , true

11_x + 10_y = 5₁₀
1(9)+1 + 1(-4)+0 = 5
9 - 4 = 5 , true

Answer 2

Cleared