Calculate the value of x and y if (27x ÷ 81x+2y = 9 ,x + 4y = 0
-
A.
x = 1, y = 1/2 -
B.
x = 2, y = – 1/2 -
C.
x − 0, y = 1 -
D.
x = 2, y = –1
Correct Answer: Option B
Explanation
(27^x ÷ 81^{(x + 2y)} = 9 \
(27)x = 9 × 81^{(x+2y)} \
(3^3 )^x =32 times 3^{4(x + 2y)} \
=3^{(2 + 4x + 8y)}\
3^{3x} = 3^{ (2 + 4x + 8y)}\
3x = 2 + 4x + 8y\
3x − 4x − 8y = 2 … … … (1)\
x + 4y = 0 … … … (2)\
− 4y = 2\
y = (− 2) ÷ 4 = − ½\
y = − ½\ )
Substitute the value of y into equation (2)
i.e x + 4y = 0
x + 4( − 1/2) = 0
x − 2 = 0
x = 2
∴ x = 2,y = − ½)
Method II
( 27^x ÷ 31^{(x + 2y) }= 9\
3^{3x} × 3^{( − 4x − 8y)} = 32\
3^{(3x − 8y)} = 32\
− x − 8y=2 ……… (1)\
x + 4y = 0 ……… (2)\
− 4 = 2\
y= 2/4 = ½\
y = ½ )
Substitute the value of y into equation 2
x + 4y=0
x + 4 (− 1) ÷ 2) = 0
x − 2 = 0
x = 2
x = 2, y = ½
There is an explanation video available below.