10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

The values of x and y for the following pair of linear \[41x+53y=135\] and \[53x+41y=147\]

A) \[x=2,y=3\]

B) \[x=1,y=2\]

C) \[x=3,y=2\]

D) \[x=2,y=1\]

Correct Answer: D

Solution :

Given pair of linear equations is

\[41x\text{ }+53y\text{ }=135\] ...(i)

and \[53x+41y=147\] ...(ii)

On adding Eqs. (i) and (ii), we get

\[94\text{ }x+\text{ }94\text{ }y\text{ }=282\]

\[\Rightarrow \,\,\,x+y=3\]

[dividing both sides by 94] ...(iii)

On subtracting Eqs. (i) from (ii), we get

\[12x-12y=12\]

\[\Rightarrow \,\,x-y=1\]

[dividing both sides by 12] ... (iv)

Now, adding Eqs. (iii) and (iv), we get

\[2x=4\,\,\,\Rightarrow \,x=2\]

On substituting x = 2 in Eq. (iii), we get

\[y=3-2=1\]

Hence, x = 2 and y = 1 is the required solution.