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

If \[ax+by={{a}^{2}}-{{b}^{2}}\] and \[bx+ay=0,\] then value of \[\text{x+y}\] is:

A) \[a+b\]

B) \[a-b\]

C) 0

D) 1

Correct Answer: B

Solution :

[b] Given equations are

\[ax+by={{a}^{2}}-{{b}^{2}}\] ...(1) and \[bx+ay=0\] ...(2)

On adding both equations, we get

\[(ax+by)+(bx+ay)={{a}^{2}}-{{b}^{2}}\]

\[\Rightarrow \,\,\,\,\,(a+b)x+(a+b)={{a}^{2}}-{{b}^{2}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,(a+b)\,\,(x+y)=(a+b)\,(a-b)\]

Hence, \[x+y=a-b\]