Answer:
(0,-5) and (-4,3)
Step-by-step explanation:
The given equations are
[tex]\left \{ {{x^2+y^2=25} \atop {2x+y=-5}} \right.[/tex]
Make y the subject in the second equation;
[tex]y=-2x-5[/tex]
Substitute into the first equation;
[tex]x^2+(-2x-5)^2=25[/tex]
Expand:
[tex]x^2+4x^2+20x+25=25[/tex]
[tex]x^2+4x^2+20x+25-25=0[/tex]
[tex]5x^2+20x=0[/tex]
[tex]5x(x+4)=0[/tex]
[tex]\Rightarrow x=0,x=-4[/tex]
When x=0,
[tex]y=-2(0)-5=-5[/tex]
This gives; (0,-5)
When x=-4
[tex]y=-2(-4)-5=3[/tex]
This gives (-4,3)
