{ 5 x + 4 y = 13 2 ∗ 5 x − 4 y = 2 {\displaystyle {\begin{cases}5^{x}+4^{y}=13\\2*5^{x}-4^{y}=2\\\end{cases}}}
{ 5 x + 4 y = 13 4 y = 13 − 5 x {\displaystyle {\begin{cases}5^{x}+4^{y}=13\\4^{y}=13-5^{x}\end{cases}}}
נציב: { 2 ∗ 5 x − 4 y = 2 2 ∗ 5 x − ( 13 − 5 x ) = 2 2 ∗ 5 x − 13 + 5 x = 2 3 ∗ 5 x = 15 5 x = 6 x = 1 4 y = 13 − 5 x 4 y = 13 − 54 y = 8 2 2 y = 2 3 y = 3 2 ↓ ( 1 , 3 2 ) {\displaystyle {\begin{cases}2*5^{x}-4^{y}=2\\2*5^{x}-(13-5^{x})=2\\2*5^{x}-13+5^{x}=2\\3*5^{x}=15\\5^{x}=6\\x=1\\4^{y}=13-5^{x}4^{y}=13-54^{y}=8\\2^{2y}=2^{3}\\y={\frac {3}{2}}\\\downarrow \\(1,{\frac {3}{2}})\\\end{cases}}}
