Answer to Question #147050 in Molecular Physics | Thermodynamics for Abdulazeez

Question

x^x + y^y = 3
x + y = 5

Find the value of x and y

Answer 1

The question is actually

$x^x + y^y = 31\\ x + y = 5$

not,

$x^x + y^y = 3\\ x + y = 5\\$

The best way to solve this is graphically,

Table $x^x + y^y = 31\\$

$x|y\\ 0|3.04\\ 1|3.04\\ 2|3\\ 3|0\\$

Table $x + y = 5$

$x|y\\ 0|5\\ 1|4\\ 2|3\\ 3|2\\$

The points of intersection are (2,3) and (3,2)

$\therefore$ $x=2$ or $3$

$y=3$ or $2$