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

If \[x=a\] and \[y=b\] is the solution of the equations \[\text{x}-\text{y}=\text{2}\]and \[\text{x}+\text{y}=\text{4},\]then the values of a and b are, respectively: (NCERT EXEMPLAR)

A) 3 and 5

B) 5 and 3

C) 3 and 1

D) \[-1\] and \[-1\]

Correct Answer: C

Solution :

[c] Since \[x=a\] and \[y=b\] is the solution of the equations

\[x-y=2\] and \[x+y=4,\]

so \[a-b=2\] ...(1)

and \[a+b=4\] ...(2)

On adding eqs. (1) and (2), we get

\[2a=6\Rightarrow a=3\]

Substituting the value of o in eq. (1), we get

\[3-b=2\Rightarrow b=1\]