Question

What is one of the solutions to the following system of equations?

Answer 1

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 .

Answer 2

That would be A

check...(8,-1)
y^2 + x^2 = 65
-1^2 + 8^2 = 65
1 + 64 = 65
65 = 65 (correct)

y + x = 7....(8,-1)
-1 + 8 = 7
7 = 7 (correct)