Calculate the value of x and y if 27x ÷…

Question 1 Report

Calculate the value of x and y if 27x ÷ 81x+2y = 9, x + 4y = 0

x = 1, y = 1/2

x = 2, y = – 1/2

x − 0, y = 1

x = 2, y = –1

Answer Details

27^{x} \div 81^{(x + 2 y)} = 9

(27) x = 9 \times 81^{(x + 2 y)}

(3^{3})^{x} = 3^{2} \times 3^{4 (x + 2 y)}

= 3^{(2 + 4 x + 8 y)}

3^{3 x} = 3^{(2 + 4 x + 8 y)}

3 x = 2 + 4 x + 8 y

3 x - 4 x - 8 y = 2 . . . . . . . . (1)

x + 4 y = 0 . . . . . . . . (2)

- 4 y = 2

y = (- 2) \div 4 = - \frac{1}{2}

y = - \frac{1}{2}

Substitute the value of y into equation (2)
i.e

x + 4 y = 0

x + 4 (- \frac{1}{2}) = 0

x - 2 = 0

x = 2

∴ x = 2, y = - \frac{1}{2}

Method II

27^{x} \div 31^{(x + 2 y)} = 9

3^{3 x} \times 3^{(- 4 x - 8 y)} = 3^{2}

3^{(3 x - 8 y)} = 3^{2}

- x - 8 y = 2 . . . . . . . . (1)

x + 4 y = 0 . . . . . . . . (2)

- 4 y = 2

y = - \frac{2}{4} = - \frac{1}{2}

y = - \frac{1}{2}

Substitute the value of y into equation 2

x + 4 y = 0

x + 4 (- 1) \div 2) = 0

x - 2 = 0

x = 2

x = 2, y = - \frac{1}{2}

Calculate the value of x and y if 27x ÷ 81x+2y = 9, x + 4y = 0