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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

Natural numbers

Vedclass · Answer

(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:

Similar Questions

Write the following equation in the standard form $ax + by + c = 0$ and indicate the values of $a, b,$ and $c$ in each case: $2x = 3y$.

Let $y$ vary directly as $x$. If $y=12$ when $x=4$,then write a linear equation. What is the value of $y$ when $x=5$?

Write the linear equation such that each point on its graph has an ordinate $3$ times its abscissa.

Any point on the $y$-axis is of the form

Find the value of $k$ if $(5, 2)$ is a solution of $3x + ky = 25$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module