Asked by Segun Adegoke
Solve the simultaneous equation 11 base x +10 base y = 5 base 10 and 13 base x + 7 base y = 19 base 10
Answers
Answered by
mathhelper
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<sub>x</sub> + 7<sub>y</sub> = 19<sub>10</sub>
and if x = 9 and y = -4
1(9)+3 + 7 = 19 , true
11<sub>x</sub> + 10<sub>y</sub> = 5<sub>10</sub>
1(9)+1 + 1(-4)+0 = 5
9 - 4 = 5 , true
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<sub>x</sub> + 7<sub>y</sub> = 19<sub>10</sub>
and if x = 9 and y = -4
1(9)+3 + 7 = 19 , true
11<sub>x</sub> + 10<sub>y</sub> = 5<sub>10</sub>
1(9)+1 + 1(-4)+0 = 5
9 - 4 = 5 , true
Answered by
Habeeb
Cleared
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