Answer
Verified
492.9k+ views
Hint: Here we have an equation with two variables. To find out the solution try to establish a relation between the variables and check the options one by one.
Complete step-by-step answer:
Let us first take the given equation:
$7x+12y=220...........(1)$
Now look at the equation very carefully, there are two variables. Variable is basically a symbol for a number we don’t know yet or we can say unknown. Here $x,y$ are unknowns to us. We have to find out some specific integer values for $x,y$.
Generally for two variables if we have two equations we get a unique solution. Here we have only one equation but two variables. So basically if we put any integer value for one variable then we will get a value for another variable.
Now, let us find out the relation between $x$ and $y$ .
The equation is:
$7x+12y=220$
Take $12y$ from left side to right side:
$\Rightarrow 7x=220-12y$
Divide both the sides by 7:
$\Rightarrow \dfrac{7x}{7}=\dfrac{220-12y}{7}$
$\Rightarrow x=\dfrac{220-12y}{7}......(2)$
If we put any value for $y$ we will always get a value of $x$ .
Here we have four options. So, we will put the values of y from the options one by one and we will check if the value of $x$ is correct or not.
Our first option is $\left( 2,24 \right)$ . So here $y=24$
Let us put the value of y in equation (2)
$\begin{align}
& x=\dfrac{220-\left( 12\times 24 \right)}{7} \\
& \Rightarrow x=\dfrac{220-288}{7} \\
& \Rightarrow x=\dfrac{-8}{7} \\
\end{align}$
So for $y=24$ , $x\ne 2$ . Hence option (a) is not correct.
Our second option is $\left( 28,2 \right)$ . So here $y=2$
Let us put the value of y in equation (2)
$\begin{align}
& x=\dfrac{220-\left( 12\times 2 \right)}{7} \\
& \Rightarrow x=\dfrac{220-24}{7} \\
& \Rightarrow x=\dfrac{196}{7}=28 \\
\end{align}$
So for $y=2$ , $x=28$ . Hence option (b) is correct.
Our third option is $\left( 32,3 \right)$ . So here $y=3$
Let us put the value of y in equation (2)
$\begin{align}
& x=\dfrac{220-\left( 12\times 3 \right)}{7} \\
& \Rightarrow x=\dfrac{220-36}{7} \\
& \Rightarrow x=\dfrac{184}{7}=26\dfrac{2}{7} \\
\end{align}$
So for $y=3$ , $x\ne 32$ . Hence option (c) is not correct.
Our fourth option is $\left( 2,34 \right)$ . So here $y=34$
Let us put the value of y in equation (2)
$\begin{align}
& x=\dfrac{220-\left( 12\times 34 \right)}{7} \\
& \Rightarrow x=\dfrac{220-408}{7} \\
& \Rightarrow x=\dfrac{-188}{7} \\
\end{align}$
So for $y=34$ , $x\ne 2$ . Hence option (d) is not correct.
Therefore, option (b) is the correct answer.
Note: We can also directly put the values from the options in the left hand side of the equation:
$7x+12y=220$ , and check if it is coming 220 or not.
Like if we substitute $\left( 28,2 \right)$ in the left hand side we will get:
$=\left( 7\times 28 \right)+\left( 12\times 2 \right)=196+24=220$
Hence, option (b) is correct.
Complete step-by-step answer:
Let us first take the given equation:
$7x+12y=220...........(1)$
Now look at the equation very carefully, there are two variables. Variable is basically a symbol for a number we don’t know yet or we can say unknown. Here $x,y$ are unknowns to us. We have to find out some specific integer values for $x,y$.
Generally for two variables if we have two equations we get a unique solution. Here we have only one equation but two variables. So basically if we put any integer value for one variable then we will get a value for another variable.
Now, let us find out the relation between $x$ and $y$ .
The equation is:
$7x+12y=220$
Take $12y$ from left side to right side:
$\Rightarrow 7x=220-12y$
Divide both the sides by 7:
$\Rightarrow \dfrac{7x}{7}=\dfrac{220-12y}{7}$
$\Rightarrow x=\dfrac{220-12y}{7}......(2)$
If we put any value for $y$ we will always get a value of $x$ .
Here we have four options. So, we will put the values of y from the options one by one and we will check if the value of $x$ is correct or not.
Our first option is $\left( 2,24 \right)$ . So here $y=24$
Let us put the value of y in equation (2)
$\begin{align}
& x=\dfrac{220-\left( 12\times 24 \right)}{7} \\
& \Rightarrow x=\dfrac{220-288}{7} \\
& \Rightarrow x=\dfrac{-8}{7} \\
\end{align}$
So for $y=24$ , $x\ne 2$ . Hence option (a) is not correct.
Our second option is $\left( 28,2 \right)$ . So here $y=2$
Let us put the value of y in equation (2)
$\begin{align}
& x=\dfrac{220-\left( 12\times 2 \right)}{7} \\
& \Rightarrow x=\dfrac{220-24}{7} \\
& \Rightarrow x=\dfrac{196}{7}=28 \\
\end{align}$
So for $y=2$ , $x=28$ . Hence option (b) is correct.
Our third option is $\left( 32,3 \right)$ . So here $y=3$
Let us put the value of y in equation (2)
$\begin{align}
& x=\dfrac{220-\left( 12\times 3 \right)}{7} \\
& \Rightarrow x=\dfrac{220-36}{7} \\
& \Rightarrow x=\dfrac{184}{7}=26\dfrac{2}{7} \\
\end{align}$
So for $y=3$ , $x\ne 32$ . Hence option (c) is not correct.
Our fourth option is $\left( 2,34 \right)$ . So here $y=34$
Let us put the value of y in equation (2)
$\begin{align}
& x=\dfrac{220-\left( 12\times 34 \right)}{7} \\
& \Rightarrow x=\dfrac{220-408}{7} \\
& \Rightarrow x=\dfrac{-188}{7} \\
\end{align}$
So for $y=34$ , $x\ne 2$ . Hence option (d) is not correct.
Therefore, option (b) is the correct answer.
Note: We can also directly put the values from the options in the left hand side of the equation:
$7x+12y=220$ , and check if it is coming 220 or not.
Like if we substitute $\left( 28,2 \right)$ in the left hand side we will get:
$=\left( 7\times 28 \right)+\left( 12\times 2 \right)=196+24=220$
Hence, option (b) is correct.
Recently Updated Pages
Identify the feminine gender noun from the given sentence class 10 english CBSE
Your club organized a blood donation camp in your city class 10 english CBSE
Choose the correct meaning of the idiomphrase from class 10 english CBSE
Identify the neuter gender noun from the given sentence class 10 english CBSE
Choose the word which best expresses the meaning of class 10 english CBSE
Choose the word which is closest to the opposite in class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Change the following sentences into negative and interrogative class 10 english CBSE
How much time does it take to bleed after eating p class 12 biology CBSE