Question

If both 'x' and 'y' are natural numbers, the equation 2x + 5y = 7 will have a unique solution.

• A. True
• B. False

Answer 1

The correct option is A True

When $x=1$,
$2+5y=7$
$\Rightarrow$ y = 1

When $x=2$,
$4+5y=7$
$\Rightarrow y=\frac{3}{5}$

When $x=3$,
$6+5y=7$
$\Rightarrow y=\frac{1}{5}$

When $x=4$,
$8+5y=7$
$\Rightarrow y=\frac{-1}{5}$

So, in natural numbers, when x>1, the value of y is <1 and progressively decreases, and then becomes negative at x = 4.

When $y=2$,
$2x+10=7$
$\Rightarrow y=\frac{-3}{2}$

When $y=3$,
$2x+15=7$
$\Rightarrow y=-4$

In natural numbers, when y>1, x<0 and progressively decreases.

Hence, in natural numbers, there is only one pair i.e., (1,1) which satisfy the given equation but in real numbers and rational numbers there are many pairs to satisfy the given linear equation.