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