If (4)x + y = 1 and (4)x – y = 4, then the value of x and y will be

1.	If (4)x + y = 1 and (4)x – y = 4, then the value of x and y will be respectively : (a)\(\frac{1}{2}\) and \(-\frac{1}{2}\)(b) \(\frac{1}{2}\) and \(\frac{1}{2}\)(c) \(-\frac{1}{2}\) and \(-\frac{1}{2}\)(d) \(-\frac{1}{2}\) and \(\frac{1}{2}\)
Answer» (a) \(\frac{1}{2} \) and \(-\frac{1}{2} \) (4)^{x + y}= 1 \(\Rightarrow\) (4)^{x + y} = 4⁰\(\Rightarrow\) x + y = 0 .........(i) (4)^{(x – y)} = 4 \(\Rightarrow\) (4)^{x – y} = 4¹\(\Rightarrow\) x – y = 1 .........(ii) Adding eqn (i) and (ii), 2x = 1 \(\Rightarrow\) x = \(\frac{1}{2}\) \(\therefore\) From eqn (i),\(\frac{1}{2}\) + y = 0 \(\Rightarrow\) y = -\(\frac{1}{2}\)

If (4)x + y = 1 and (4)x – y = 4, then the value of x and y will be respectively : (a)\(\frac{1}{2}\) and \(-\frac{1}{2}\)(b) \(\frac{1}{2}\) and \(\frac{1}{2}\)(c) \(-\frac{1}{2}\) and \(-\frac{1}{2}\)(d) \(-\frac{1}{2}\) and \(\frac{1}{2}\)

Answer»

(a) \(\frac{1}{2} \) and \(-\frac{1}{2} \)

(4)^{x + y}= 1 \(\Rightarrow\) (4)^{x + y} = 4⁰\(\Rightarrow\) x + y = 0 .........(i)

(4)^{(x – y)} = 4 \(\Rightarrow\) (4)^{x – y} = 4¹\(\Rightarrow\) x – y = 1 .........(ii)

Adding eqn (i) and (ii), 2x = 1

\(\Rightarrow\) x = \(\frac{1}{2}\)

\(\therefore\) From eqn (i),\(\frac{1}{2}\) + y = 0

\(\Rightarrow\) y = -\(\frac{1}{2}\)