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

If \[\text{3x}-\text{2y}=\text{4}\] and \[\text{2x}+\text{y}=\text{5},\] then the value of m such that \[\text{y}=\text{x}+\text{m},\] is:

A) \[m=-1\]

B) \[m=1\]

C) \[m=-\frac{1}{2}\]

D) \[m=\frac{1}{2}\]

Correct Answer: A

Solution :

[a] The given pair of equations is

\[3x-2y=4\,\,\,\Rightarrow \,\,\,3x-2y-4=0\] ...(1)

and \[2x+y=5\,\,\,\Rightarrow \,\,2x+y-5=0\] ...(2)

Multiplying eq. (2) by 2, we get

\[4x+2y-10=0\] ...(3)

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

\[7x-14=0\,\,\,\Rightarrow \,\,\,x=2\]

Substituting x = 2 in eq. (1), we get

\[3(2)-2y-4=0\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,2y=2\Rightarrow y=1\]

Now, \[y=x+m\,\,\,\,\Rightarrow \,\,\,1=2+m\,\,\Rightarrow \,\,m=-1\]