The solution to the system of equations are -1 and ±√5
Given the systems of equations;
[tex]x^2 + y^2 = 6\\ x^2 - y = 6[/tex]
From equation 2;
[tex]x^2 = 6 + y[/tex]..................................... 3
Substitute equation 3 into 1 to have:
[tex]6+y+y^2=6y^2+y=6-6\\y^2+y=0\\y^2=-y\\y = -1[/tex]
Substitute y = -1 into equation 3
[tex]x^2 = 6 + y\\x^2 = 6 + (-1)\\x^2 = 6 -1\\x^2=5\\x=\pm \sqrt{5}[/tex]
Hence the solution to the system of equations are -1 and ±√5
Learn more on systems of equation here: https://brainly.com/question/13729904
