Question

Find the value of the ratio x over y if the equation is 5x²-13xy+8y²=0 ​

Answer 1

Answer:

$\frac{x}{y} = \frac{8}{5}$

Step-by-step explanation:

Given

$5x^2 - 13xy + 8y^2 = 0$

Required

Find x/y

$5x^2 - 13xy + 8y^2 = 0$

Expand

$5x^2 -5xy - 8xy + 8y^2 = 0$

Factorize:

$5x(x - y) - 8y(x - y) = 0$

Factor out x - y

$(5x - 8y)(x - y) = 0$

Divide both sides by $(x-y)$

$5x - 8y = 0$

Add 8y to both sides

$5x = 8y$

Divide both sides by 5

$x = \frac{8}{5}y$

Divide both sides by y

$\frac{x}{y} = \frac{8}{5}$