The equation 2x + 5y = 7 has a unique solutio | vedclass

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(B) For the linear equation $2x + 5y = 7$,we look for solutions where $x$ and $y$ are natural numbers (i.e.,$x, y \in \{1, 2, 3, ...\}$).If $x = 1$,th

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Natural numbers

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(B) For the linear equation $2x + 5y = 7$,we look for solutions where $x$ and $y$ are natural numbers (i.e.,$x, y \in \{1, 2, 3, ...\}$).If $x = 1$,then $2(1) + 5y = 7$,which gives $5y = 5$,so $y = 1$.If $x = 2$,then $2(2) + 5y = 7$,which gives $4 + 5y = 7$,so $5y = 3$,or $y = 3/5$,which is not a natural number.If $x \ge 2$,$5y$ would be $7 - 2x \le 3$,meaning $y$ would not be a natural number.Thus,the only pair of natural numbers that satisfies the equation is $(1, 1)$,making it a unique solution.

The equation $2x + 5y = 7$ has a unique solution,if $x, y$ are:

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