Answer: {(5,0), (3,4)}
Step-by-step explanation:
You can apply the Substitution method:
- Solve for y from the second equation.
- Substitute into the first equation and solve for x.
Then:
[tex]y=10-2x[/tex]
[tex]x^2+y^2=25\\x^2+(10-2x)^2=25\\[/tex]
(Remember that: [tex](a\±b)^2=a^2\±2ab+b^2[/tex])
[tex]x^2+(10^2-2(10)(2x)+(2x)^2)=25\\x^2+100-40x+4x^2=25\\5x^2-40x+75=0\\x^2-8x+15=0\\(x-5)(x-3)=0\\\\x=5\\x=3[/tex]
Substitute the values obtained into one of the original equation and solve for y:
[tex]2(5)+y=10\\10+y=10\\y=0\\\\2(3)+y=10\\6+y=10\\y=4[/tex]
The solution set is: {(5,0), (3,4)}
