Question

2^{x} + 3^{y}=17
2^{x+2} - 3^{y+1} = 5
what is value of x and y

Answer 1

$let\ 2^x\ be\ a,\ \ and\ \ 3^y\ \ be\ \ b \\ \\ 2^x + 3^y = 17 \ \ \ \ \ and, \ \ \ \ \ 2^{x+2} - 3^{y+1} = 5 \\ \\ a + b = 17\ \ \ \ -\ equation\ 1 \\ \\ 2^x\ 2^2 - 3^y * 3^1 = 5 \\ \\ 4 * 2^x - 3 * 3^y = 5 \\ \\ 4 a - 3 b= 5 \ \ \ - equation\ 2 \\ \\ Multiply\ equation\ 1\ by\ 3\ and\ add\ to\ equation\ 2,\ we\ get \\ \\ 7a = 51+5 = 56 \\ \\ a = 8 \\ \\ From\ equation\ 1\ we\ get\ b = 9$