[tex]x=\sqrt{6}, y=0\\ x=-\sqrt{6} , y=0\\x=\sqrt{5} , y=-1\\x=-\sqrt{5} , y=-1[/tex]
Or as ordered pairs: [tex](\sqrt{6} ,0),(-\sqrt{6} ,0),(\sqrt{5} ,-1),(-\sqrt{5} ,-1)[/tex]
Lets solve our system of equations step by step
[tex]x^2+y^2=6[/tex] equation (1)
[tex]x^2-y=6[/tex] equation (2)
1. Solve for [tex]x^2[/tex] in equation (2)
[tex]x^2-y=6[/tex]
[tex]x^2=6+y[/tex] equation (3)
2. Replace equation (3) in equation (1) and solve for [tex]y[/tex]
[tex]x^2+y^2=6[/tex]
[tex]6+y+y^2=6[/tex]
[tex]y^2+y=0[/tex]
[tex]y(y+1)=0[/tex]
[tex]y=0[/tex] or [tex]y=-1[/tex]
3. Replace the values of [tex]y[/tex] in equation (3) and solve for [tex]x[/tex]
- For [tex]y=0[/tex]
[tex]x^2=6+y[/tex]
[tex]x^2=6[/tex]
[tex]x=\sqrt{6}[/tex] or [tex]x=-\sqrt{6}[/tex]
- For [tex]y=-1[/tex]
[tex]x^2=6+y[/tex]
[tex]x^2=6-1[/tex]
[tex]x^2=5[/tex]
[tex]x=\sqrt{5}[/tex] or [tex]x=-\sqrt{5}[/tex]
So, the solutions of our system of equation are:
[tex]x=\sqrt{6}, y=0\\ x=-\sqrt{6} , y=0\\x=\sqrt{5} , y=-1\\x=-\sqrt{5} , y=-1[/tex]
Answer:
(√6,0)
(√5,-1)
(-√6,0)
(-√5,-1)
Step-by-step explanation:
Edg 2021
