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. |
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