Question

7y - 2 / 5y - 1 = 3 + 7 y / 4+ 5 y ​

Answer 1

Given :

• The given expression :

$\\ \bullet \bf \: \frac{7y - 2}{5y - 1} = \frac{3 + 7y}{4 + 5y}$

To Find :

• The value of y in this expression =?

Solution :

•The given expression is

$\\ \bullet \sf \: \frac{7y - 2}{5y - 1} = \frac{3 + 7y}{4 + 5y}$

By Cross multiplication on both sides :

$\\ \implies \sf \: \frac{7y - 2}{5y - 1} = \frac{3 + 7y}{4 + 5y} \\ \\ \\ \implies \sf \: \bigg((7y - 2)(4 + 5y) \bigg) = \bigg((5y - 1)(3 + 7y) \bigg) \\ \\ \\ \implies \sf \bigg((7y(4 + 5y) - 2(4 + 5y) \bigg) = \bigg((5y(3 + 7y) - 1(3 + 7y) \bigg) \\ \\ \\ \implies \sf \: \bigg(28y + 35 {y}^{2} - 8 - 10y \bigg) = \bigg(15y + 35 {y}^{2} - 3 - 7y \bigg) \\ \\ \\ \implies \sf \: \bigg(18y + 35 {y}^{2} - 8 \bigg) = \bigg(8 y + 35 {y}^{2} - 3 \bigg) \\ \\ \\ \implies \sf \: 18y + 35 {y}^{2} - 8 - 8y - 35 {y}^{2} + 3 = 0 \\ \\ \\ \implies \sf \: 10y - 5 = 0 \\ \\ \\ \implies \sf \: y = \frac{5}{10} = \frac{1}{2} \\ \\ \\ \\ \implies \boxed{ \sf{y = \frac{1}{2} }}$

The value of y is

$\bullet\boxed{ \sf{y = \frac{1}{2} }}$

Answer 2

Answer:

$\frac{7y - 2}{5y - 1} = \frac{3 + 7y}{4 + 5y} \\ (7y - 2)(4 + 5y) = (3 + 7y)(5y - 1) \\ 28y + 35y {}^{2} - 8 - 10y = 15y - 3 + 35y {}^{2} - 7y \\ 35 {y}^{2} \: cancel \: on \: both \: sides \: we \: get \\ 18y - 8 = 8y - 3 \\ 18y - 8y = 8 - 3 \\ 10y = 5 \\ y = \frac{5}{10} \\ = \frac{1}{2}$

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