Question

Розв`язати системи рівнянь:
(x + y = 7
(x^2 + y^2 = 25

Answer 1

$\left \{ {{x+y=7} \atop {x^{2}+y^{2} =25}} \right. \\\left \{ {{y=7-x} \atop {x^{2}+(7-x)^{2}=25 }} \right. \\\left \{ {{y=7-x} \atop {x^{2} +49-14x+x^{2} =25}} \right. \\\left \{ {{y=7-x} \atop {2x^{2}-14x+24=0}} \right. \\\left \{ {{y=7-x} \atop {x^{2}-7x+12=0}} \right. \\\left \{ {{y=7-x} \atop {(x-3)(x-4)=0}} \right. \\\\\left \{ {{y=7-x} \atop {x=3;x=4}} \right.$

x=3 ⇒ y=7-3; y=4

x=4 ⇒ y=7-4; y=3

Ответ: х₁=3; у₁=4; х₂=4; у₂=3.