Answer
Verified
416.1k+ views
Hint: The given question is related to the highest common factor of two numbers and linear equations in two variables. Find the highest common factor of \[45\] and \[27\], then draw the line represented by the equation $d=27x+45y$ on a graph and check the points that lie on the line.
Complete step-by-step answer:
To solve the question, first we have to find the highest common factor of \[45\] and \[27\]. We will use the factorization method to find the value of the highest common factor of \[45\] and \[27\]. In factorization method, we write the numbers as a product of prime numbers and then find the highest number that is common in both.
\[45\] can be written as $45=3\times 3\times 5$ and \[27\] can be written as $27=3\times 3\times 3$. We can see that the highest number common in both is $3\times 3=9$. So, the highest common factor of \[45\] and \[27\] is $9$. We are given that the highest common factor of \[45\] and \[27\] is $d$ . So, $d=9$.
Now, we are given the equation $d=27x+45y$. Substituting $d=9$ in the equation, we get $9=27x+45y$. On rearranging the equation to make it of the form $y=mx+c$, we get $y=\dfrac{-27}{45}x+\dfrac{1}{5}$. So, the equation represents a line with slope $m=\dfrac{-27}{45}$ and $y$ intercept $c=\dfrac{1}{5}$.
The line is shown on the graph as:
Now, we will plot the points corresponding to the given options on the line. The points lying on the line will satisfy the equation $d=27x+45y$. The points corresponding to the options are:
Option A. $(2,1)$ ; Option B. $(2,-1)$ ; Option C. $(-1,2)$; Option D. $(-1,-2)$.
The points are plotted on the graphs as:
From the graph we can see that $B(2,-1)$ is the only point lying on the line. So, the values of $x$ and $y$ satisfying $d=27x+45y$ are $x=2,y=-1$, where $d$ is the highest common factor of \[45\] and \[27\].
Hence, option B. is the correct answer.
Note: The correct answer can also be found by substituting the values of $x$ and $y$ from each option in the equation. But it will be time taking. So, it is better to plot the line and points on the graph to find the values of $x$ and $y$ satisfying the equation.
Complete step-by-step answer:
To solve the question, first we have to find the highest common factor of \[45\] and \[27\]. We will use the factorization method to find the value of the highest common factor of \[45\] and \[27\]. In factorization method, we write the numbers as a product of prime numbers and then find the highest number that is common in both.
\[45\] can be written as $45=3\times 3\times 5$ and \[27\] can be written as $27=3\times 3\times 3$. We can see that the highest number common in both is $3\times 3=9$. So, the highest common factor of \[45\] and \[27\] is $9$. We are given that the highest common factor of \[45\] and \[27\] is $d$ . So, $d=9$.
Now, we are given the equation $d=27x+45y$. Substituting $d=9$ in the equation, we get $9=27x+45y$. On rearranging the equation to make it of the form $y=mx+c$, we get $y=\dfrac{-27}{45}x+\dfrac{1}{5}$. So, the equation represents a line with slope $m=\dfrac{-27}{45}$ and $y$ intercept $c=\dfrac{1}{5}$.
The line is shown on the graph as:
Now, we will plot the points corresponding to the given options on the line. The points lying on the line will satisfy the equation $d=27x+45y$. The points corresponding to the options are:
Option A. $(2,1)$ ; Option B. $(2,-1)$ ; Option C. $(-1,2)$; Option D. $(-1,-2)$.
The points are plotted on the graphs as:
From the graph we can see that $B(2,-1)$ is the only point lying on the line. So, the values of $x$ and $y$ satisfying $d=27x+45y$ are $x=2,y=-1$, where $d$ is the highest common factor of \[45\] and \[27\].
Hence, option B. is the correct answer.
Note: The correct answer can also be found by substituting the values of $x$ and $y$ from each option in the equation. But it will be time taking. So, it is better to plot the line and points on the graph to find the values of $x$ and $y$ satisfying the equation.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE