Answer:
Therefore the solutions are
[tex]x=0\\and\\ y =5\\\\Or\\\\x=-4\\and\\y=-3[/tex]
Step-by-step explanation:
Given:
[tex]x^{2} + y^{2} =25[/tex] .........( 1 )
[tex]y-2x = 5\\y=2x+5[/tex] ................( 2 )
To Find:
x = ?
y = ?
Solution:
Substituting ' y ' in Equation 1 we get
[tex]x^{2}+(2x+5)^{2} =25[/tex]
Using identity (A+B)²=A²+2AB+B² we get
[tex]x^{2}+4x^{2}+20x+25=25\\\\5x^{2}+20x=0\\5x(x+4)=0\\5x=0\ or\ x+4=0\\x=0\ or\ x= -4[/tex]
Now Substitute x =0 in equation 2 we get
[tex]y=2\times 0+5=5[/tex]
Or
Now Substitute x =-4 in equation 2 we get
[tex]y=2\times -4+5=-3[/tex]
Therefore the solutions are
[tex]x=0\\and\\ y =5\\\\Or\\\\x=-4\\and\\y=-3[/tex]
