| Directions (Q. Nos. 1 - 22): In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as: |
| Assertion (A): \[\text{x}=\text{2},\text{ y}=\text{1}\]is a solution of pair of equations \[\text{3x}-\text{2y}=\text{4}\]and\[\text{2x}+\text{y}=\text{5}\]. |
| Reason (R): A pair of values \[(x,y)\] satisfying each one of the equations in a given system of two simultaneous linear equations in x and y is called a solution of the system of equations. |
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
Correct Answer: A
Solution :
| [a] The given system of equations is |
| \[3x-2y=4\] ...(1) |
| \[2x+y=5\] ...(2) |
| Putting \[x=2\] and \[y=1\] in eq. (1), we get |
| \[LHS=3\times 2-2\times 1=4=RHS\] |
| Putting \[x=2\] and \[y=1\] in eq. (2), we get |
| \[LHS=2\times 2+1\times 1=5=RHS\] |
| Thus, \[x=2\] and \[y=1\] satisfy both the equations of the given system. |
| Hence, \[x=2,y=1\] is a solution of the given pair of equations. |
| So, Assertion: True; Reason: True and it is the correct explanation of assertion. |
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