Question

If $x=a,y=b$ is the solution of the systems of equations $x-y=2$ and $x+y=4$ , then the values of $a$ and $b$ are, respectively

(a) 3 and 1 (b) 3 and 5 (c) 5 and 3 (d) $-$ 1 and $-$3

Answer 1

The given equations are
$$\begin{gathered} x-y=2.....\left(1\right) \\ x+y=4.....\left(2\right) \end{gathered}$$
Adding (1) and (2), we get
2x = 6
⇒ x = 3
Putting x = 3 in (1), we get
3 + y = 4
⇒ y = 1
So, x = a = 3 and y = b = 1.
Thus, the values of a and b are 3 and 1, respectively.

Hence, the correct answer is option (a).