Question

Solve the following system. x^2 + y^2= 25
2x + y = 10 The solution set is...?

Answer 1

$x^2 + y^2= 25\\ 2x+y=10\\\\ x^2 + y^2= 25\\ y=10-2x\\\\ x^2+(10-2x)^2=25\\ x^2+100-40x+4x^2=25\\ 5x^2-40x+75=0\\ x^2-8x+15=0\\ x^2-3x-5x+15=0\\ x(x-3)-5(x-3)=0\\ (x-5)(x-3)=0\\ x=5 \vee x=3\\\\ y=10-2\cdot5 \vee y=10-2\cdot3\\ y=0 \vee y=4\\\\ \boxed{(x,y)=\{(3,4),(5,0)\}}$