Question

1. given that the equation \\(\frac{4x - 3y}{x + y} = \frac{3}{2}\\) is true, what is the value of \\(\frac{y}{x}\\)?\

a. \\(\frac{5}{8}\\)\
b. \\(\frac{5}{4}\\)\
c. \\(\frac{5}{3}\\)\
d. \\(\frac{10}{11}\\)

Explanation:

Step1: Cross-multiply to eliminate fractions

$$2(4x - 3y) = 3(x + y)$$

Step2: Expand both sides of the equation

$$8x - 6y = 3x + 3y$$

Step3: Group x and y terms

$$8x - 3x = 3y + 6y$$

Step4: Simplify both sides

$$5x = 9y$$

Step5: Solve for $\frac{y}{x}$

$$\frac{y}{x} = \frac{5}{9}$$

Answer:

A. $\frac{5}{9}$