Question

If linear equation has solutions (5,-5),(0,0),(5,-5), then what is the equation?

Answer 1

If the solutions of a linear  equation are (5,-5),(0,0),(5,-5) , then the linear equation which satisfies all the solutions is :                                       
 x + y = 0
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1)  When x = 5 , y = -5   
 5 + (-5) = 0    
∴ x + y = 0
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2) When x = 0 , y = 0 
 0 + 0 = 0
∴ x + y = 0
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3)When x = -5 , y = 5     
(-5) + 5  = 0 
∴  x + y = 0
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Answer 2

Answer:

Let the linear equation be

ax + by + c = 0        ---------------    (i)

where a, b and c are constants.

The given solutions are, (5, -5), (0, 0) and (5, -5).

Putting (0, 0) solution i.e., x = 0 and y = 0 in (i), we get

a(0) + b(0) + c = 0

0 + 0 + c = 0

c = 0

Now the equation becomes,

ax + by = 0       -------------------   (ii)

Putting (5,-5) solution in (ii), we get

a(5) + b(-5) = 0

5a - 5b = 0

5(a - b) = 0

a - b = 0

a = b   --------- (a)

Now the equation becomes,

ax + ay = 0

a(x + y) = 0

x + y = 0

Hence, the linear equation is x + y = 0.

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