Problem to Solve for Unknown Variables

Topic : Simultaneous Equation

Question : Solve for x and y
x ² + y² = 25
x – y = 5

Solution :
x ² + y² = 25 ---------------------(1)
x – y = 5--------------------------(2)

+y = +y
---------------
x = 5+y

substituting x value in (1)

x ² + y² = 25
(5+y) ² + y² = 25
25 +y² +10y + y² = 25
2y² + 10y =25-25
2y(y+5) = 0
2y=0; y+5 =0
y = 0 and y = -5

Now consider x-y = 5
when y = 0 , x -0 = 5
so x = 5 and
when y = -5 , x -(-5)=5
x+5=5
x=0 (subtracting both sides by 5)