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if $(3y -5x)/(7x-4y) = 3/4$ , find the value of $x/y$

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Solve multi-step equations with fractional coefficients

Full solution

Q. if

(3y -5x)/(7x-4y) = 3/4

, find the value of

x/y

Set up equation: Set up the equation according to the given problem. $\newline$ $(\frac{3y - 5x}{7x - 4y}) = \frac{3}{4}$
Cross-multiply: Cross-multiply to eliminate the fraction. $\newline$ $(3y - 5x) \times 4 = (7x - 4y) \times 3$
Distribute numbers: Distribute the numbers on both sides of the equation. $12y - 20x = 21x - 12y$
Rearrange equation: Rearrange the equation to group like terms. $12y + 12y = 21x + 20x$
Combine like terms: Combine like terms. $\newline$ $24y = 41x$
Divide by $24$ : Divide both sides by $24$ to solve for $x/y$ . $\frac{x}{y} = \frac{24y}{41x}$
Simplify equation: Simplify the equation by dividing both sides by $y$ . $\frac{x}{y} = \frac{24}{41}$

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