Answer: x=4, y=1.
Step-by-step explanation:
[tex]\left \bigg \{ {\big{x+y=5} \atop\big {x^{2}-y^{2} =15}} \right.\\\\x+y=5\\x+y-y=5-y\\x=5-y\\\\(5-y)^{2} -y^{2} =15\\5^{2} -10y+y^{2} -y^{2}=15\\25-10y=15\\25-10y-25=15-25\\ -10y=-10\\-10y \div (-10)=-10 \div (-10)\\y=1\\\\x+y=5\\x+1=5\\x+1-1=5-1\\x=4[/tex]
