Question

How many solutions does the equation 2x + 5y = 7 have?
($x$ and $y$ are natural numbers)

• A. 0.0
• B. 1
• C. 2
• D. Infinite

Answer 1

The correct option is B 1

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, among natural numbers, when x > 1, the value of y is less than 1 and progressively decreases, and then becomes negative at x = 4.

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

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

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

Hence, there is only one pair i.e., (1, 1) which satisfies the given equation when x and y are both natural numbers.