Answer

Verified

448.2k+ 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

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths 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 many crores make 10 million class 7 maths CBSE

The 3 + 3 times 3 3 + 3 What is the right answer and class 8 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE