Answer to Question 5

 

5. x2 + y2 = 25
x - y = 5		  
Solve the linear equation for x. x = y + 5
Substitute into the quadratic equation.

 

       

Divide by 2 to get a simpler
               equation.

 (y + 5)2 + y2 = 25
y2 + 10y + 25 + y2 = 25
2y2 + 10y + 25 = 25
2y2 + 10y = 0
y2 + 5y = 0
y(y + 5) = 0
y = 0        y + 5 = 0
                y = -5
Substitute each value into the linear equation. x - y = 5

x - 0 = 5
x = 5              (5,0)

x - y = 5

x -(-5) = 5
x + 5 = 5
x = 0             (0,-5)

Solution Set is: {(5,0),(0,-5)}
 

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