5: Check graphically that system : x - y = 0 and 2x + 2y = 0 is consistent or inconsistent.
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EXPLANATION.
Check graphically.
⇒ x - y = 0. - - - - - (1).
⇒ 2x + 2y = 0. - - - - - (2).
As we know that,
From equation (1), we get.
⇒ x - y = 0. - - - - - (1).
Put the value of x = 0 in the equation, we get.
⇒ (0) - y = 0.
⇒ y = 0.
Their Co-ordinates = (0,0).
Put the value of y = 0 in the equation, we get.
⇒ x - (0) = 0.
⇒ x = 0.
Their Co-ordinates = (0,0).
From equation (2), we get.
⇒ 2x + 2y = 0. - - - - - (2).
Put the value of x = 0 in the equation, we get.
⇒ 2(0) + 2y = 0.
⇒ 2y = 0.
⇒ y = 0.
Their Co-ordinates = (0,0).
Put the value of y = 0 in the equation, we get.
⇒ 2x + 2(0) = 0.
⇒ 2x = 0.
⇒ x = 0.
Their Co-ordinates = (0,0).
Hence, the given equation is consistent.
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