Answer:
(8,-1)
Step-by-step explanation:
Given : [tex]x^{2} +y^{2} =65[/tex]
[tex]x+y=7[/tex]
To Find: solution of given system of equations.
Solution:
Equation a : [tex]x^{2} +y^{2} =65[/tex]
Equation b : [tex]x+y=7[/tex]
Substitute the value of y from equation b in equation a
y from equation b : y = 7-x
Now substitute value of y in equation a
Thus equation a becomes:
[tex]x^{2} +(7-x)^{2} =65[/tex]
[tex]x^{2} +49+x^{2}-14x =65[/tex]
[tex]2x^{2} -14x =65-49[/tex]
[tex]x^{2} -7x -8=0[/tex]
[tex]x^{2} -8x+x -8=0[/tex]
[tex]x(x-8)+1(x-8)=0[/tex]
[tex](x+1)(x-8)=0[/tex]
⇒ x= -1 and x = 8
Now substitute values of x in equation b to obtains values of y
⇒ [tex]x+y=7[/tex]
for x = -1
⇒ [tex]-1+y=7[/tex]
⇒ [tex]y=7+1[/tex]
⇒ [tex]y=8[/tex]
Thus (x,y)=(-1,8)
For x =8
⇒ [tex]8+y=7[/tex]
⇒ [tex]y=7-8[/tex]
⇒ [tex]y=-1[/tex]
Thus (x,y)=(8,-1)
Hence Option A is the correct solution .
