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

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Question

(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:

Similar Questions

The graph of the equation $3x + 7y = k$ is a line passing through the origin. Then,$k = \ldots$

Draw the graph of the following linear equation in two variables:
$2x - 3y = 0$

From the choices given below,choose the equation whose graphs are given in Fig. $(i)$ and Fig. $(ii)$.
For Fig. $(i)$:
$(a)$ $y=x$
$(b)$ $x+y=0$
$(c)$ $y=2x$
$(d)$ $2+3y=7x$
For Fig. $(ii)$:
$(a)$ $y=x+2$
$(b)$ $y=x-2$
$(c)$ $y=-x+2$
$(d)$ $x+2y=6$

Write four solutions for the following equation: $3x + 5y = 0$.

If $(3,5)$ is a solution of the equation $2x + 5y = k$,find the value of $k$.

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