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

If \[{{3}^{x-y}}=9\]and \[\text{x}-\text{2y}=\text{6}\]represent a system of the equations, then the value of \[\text{x+y}\] is:

A) \[-2\]

B) \[-6\]

C) \[-4\]

D) None of these

Correct Answer: B

Solution :

[b] We have, \[{{3}^{x-y}}=9\Rightarrow \,\,{{3}^{x-y}}={{3}^{2}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x-y=2\] ..(1)

and \[x-2y=6\] ..(2)

From eq. (1), \[x=y+2\] .....(3)

Substituting the value of x in eq. (2). we get

\[y+2-2y=6\,\,\,\Rightarrow \,\,\,-y=4\,\,\,\Rightarrow \,\,\,y=-4\]

Substituting the value of y in eq. (3), we get

\[x=-4+2=-2\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x+y=-2+(-4)=-6\]