The graph of which of the following linear equations will pass through origin a) x + y =4 b) x – y= 2 c) x= 3y d) 3 = 2x + y
Answers
Answer :
c). x = 3y
Solution :
★ Let's check whether x + y = 4 passes through origin (0,0) or not .
Putting x = 0 and y = 0 , we get ;
=> LHS = x + y
=> LHS = 0 + 0
=> LHS = 0
RHS = 4
Clearly ,
LHS ≠ RHS , thus the equation x + y = 4 doesn't passes through origin (0,0) .
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★ Let's check whether x - y = 2 passes through origin (0,0) or not .
Putting x = 0 and y = 0 , we get ;
=> LHS = x - y
=> LHS = 0 - 0
=> LHS = 0
RHS = 2
Clearly ,
LHS ≠ RHS , thus the equation x - y = 2 doesn't passes through origin (0,0) .
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★ Let's check whether x = 3y passes through origin (0,0) or not .
Putting x = 0 and y = 0 , we get ;
=> LHS = x
=> LHS = 0
=> RHS = 3y
=> RHS = 3×0
=> RHS = 0
Clearly ,
LHS = RHS , thus the equation x = 3y passes through origin (0,0) .
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★ Let's check whether 3 = 2x + y passes through origin (0,0) or not .
Putting x = 0 and y = 0 , we get ;
LHS = 3
=> RHS = 2x + y
=> RHS = 2×0 + 0
=> RHS = 0 + 0
=> RHS = 0
Clearly ,
LHS ≠ RHS , thus the equation 3 = 2x + y doesn't passes through origin (0,0) .
Hence ,
The linear equation x = 3y passes through origin.
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Note :
If an equation doesn't contain any constant term , then it always passes through origin .
The linear equation x = 3y doesn't contain any constant term , thus it passes through origin .
Answer:
Step-by-step explanation:
Let's check whether x + y = 4 passes through origin (0,0) or not .
Putting x = 0 and y = 0 , we get ;
=> LHS = x + y
=> LHS = 0 + 0
=> LHS = 0
RHS = 4
Clearly ,
LHS ≠ RHS , thus the equation x + y = 4 doesn't passes through origin (0,0) .
★ Let's check whether x - y = 2 passes through origin (0,0) or not .
Putting x = 0 and y = 0 , we get ;
=> LHS = x - y
=> LHS = 0 - 0
=> LHS = 0
RHS = 2
Clearly ,
LHS ≠ RHS , thus the equation x - y = 2 doesn't passes through origin (0,0) .
★ Let's check whether x = 3y passes through origin (0,0) or not .
Putting x = 0 and y = 0 , we get ;
=> LHS = x
=> LHS = 0
=> RHS = 3y
=> RHS = 3×0
=> RHS = 0
Clearly ,
LHS = RHS , thus the equation x = 3y passes through origin (0,0) .
★ Let's check whether 3 = 2x + y passes through origin (0,0) or not .
Putting x = 0 and y = 0 , we get ;
LHS = 3
=> RHS = 2x + y
=> RHS = 2×0 + 0
=> RHS = 0 + 0
=> RHS = 0
Clearly ,
LHS ≠ RHS , thus the equation 3 = 2x + y doesn't passes through origin (0,0)
Hence ,
The linear equation x = 3y passes through origin.
Note :
If an equation doesn't contain any constant term , then it always passes through origin .
The linear equation x = 3y doesn't contain any constant term , thus it passes through origin .