Calculate the value of x and y if 27x 81x 2y 9 ... - JAMB Mathematics 2015 Question

(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