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Question 1669 :
The number of distinct integer solutions $(x, y)$ of the equation $| x + y | + | x - y | = 2$ , is

Video Explanation

Explanatory Answer

We are thinking about two scenarios where $x \geq y$ and $x \geq - y$ . When $x \geq y$ ,

x + y + x - y = 2 2 x = 2 x = 1

So, the possibilities are ( 1,1 ), ( 1,0 ) and ( $1, - 1$ )
When $x = 0$ ,
The possibilities are $(0, 1)$ and $(0, - 1)$
When $x = - 1$
The possibilities are ( $- 1, 1$ ), ( $- 1, 0$ ) and ( $- 1, - 1$ )
So, the number of distinct integer solutions $= 8$

The question is "The number of distinct integer solutions $(x, y)$ of the equation $| x + y | + | x - y | = 2$ , is"

Hence, the answer is '8'

The question is "The number of distinct integer solutions <mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo stretchy="false">)</mo></math>">(x,y) of the equation <mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mi>x</mi><mo>+</mo><mi>y</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mi>x</mi><mo>&#x2212;</mo><mi>y</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mo>=</mo><mn>2</mn></math>">|x+y|+|x−y|=2, is"

Previous Year Papers

Question 1669 :
The number of distinct integer solutions $(x, y)$ of the equation $| x + y | + | x - y | = 2$ , is

Video Explanation

Explanatory Answer

Hence, the answer is '8'

The answer is

Choice 8 is the correct answer.

Previous Year Papers

Question 1669 : The number of distinct integer solutions (x,y) of the equation |x+y|+|x−y|=2, is

Video Explanation

Explanatory Answer

Hence, the answer is '8'

The answer is

Choice 8 is the correct answer.

Question 1669 :
The number of distinct integer solutions $(x, y)$ of the equation $| x + y | + | x - y | = 2$ , is