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

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(A) The linear equation $2x + 5y = 7$ represents a line in the Cartesian plane,which has infinitely many solutions in the set of real numbers.However,

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Natural numbers

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(A) The linear equation $2x + 5y = 7$ represents a line in the Cartesian plane,which has infinitely many solutions in the set of real numbers.However,if we restrict $x$ and $y$ to natural numbers (i.e.,$x, y \in \{1, 2, 3, ...\}$),we can test for solutions:If $x = 1$,then $2(1) + 5y = 7 \implies 5y = 5 \implies y = 1$.If $x = 2$,then $2(2) + 5y = 7 \implies 5y = 3 \implies y = 3/5$ (not a natural number).If $x \ge 2$,$y$ will not be a natural number.Thus,$(1, 1)$ is the only solution in natural numbers.

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

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