1. Solve the following pairs of equations by reducing them to a pair o

1.	1. Solve the following pairs of equations by reducing them to a pair of linear equations:7x-2y/xy=58x+7y/xy=15
Answer» AnswEr: Given Equation $\bullet\:\sf\: \dfrac{7x \:-\:2y}{xy} = 5$ $\:\:\: \sf\dfrac{8x \:+\:7y}{xy} = 15$ $:\implies\sf\: \dfrac{7x}{xy} \:-\: \dfrac{2y}{xy} = 5$ ---------[EQUATION 1] $:\implies\sf\: \dfrac{7}{y}\:-\:\dfrac{2}{x} = 5$ $:\implies\sf\: 7 \times \dfrac{1}{y}\:-\: 2 \times \dfrac{1}{x}=5$ Here, we get $\sf\dfrac{1}{y} = <klux>V</klux> \:\& \: \dfrac{1}{x} = u$ Similarly, $:\implies\sf\: \dfrac{8x}{xy}\:+\:\dfrac{7y}{xy} = 15$ ---------[Equation 2] $:\implies\sf\: \dfrac{8}{y} \:+\;\dfrac{7}{x} = 15$ $:\implies\sf\: 8 \times \dfrac{1}{y} \:+\: 7 \times \dfrac{1}{x} = 15$ Now, From Equation 1 & 2 $:\implies\sf\: 7v - 2u = 5$ ------[Equation 3] $:\implies\sf\: 8v + 7u = 15$ -----[Equation 4] Multiplying Equation Equation (3) by 7 and Equation (4) by 2 $:\implies\sf\: 7 \times [7v \:-\:2u] = 5 \times 7$ $:\implies\sf\bold{49v\: -\: 14u\: =\: 35}$ -------[Equation 5] $:\implies\sf\: 2 \times [8v \:+\:7u] = 15 \times 2$ $:\implies\sf\bold{16v\:+\:14u\:=\:30}$ --------[Equation 6] Now, From Equations 5 & 6 $:\implies\sf\: 49v - 14u = 35$ $:\implies\sf\: 16v + 14u = 30$ $:\implies\sf\: 65v = 65$ $:\implies\sf\: v = \cancel\dfrac{65}{65}$ $:\implies\boxed{\sf{\pink{v\:=\:1}}}$ $\rule{200}2$ Substituting the Value of v in Equation 3 $:\implies\sf\: 7v - 2u = 5$ $:\implies\sf\: 7(1) - 2u = 5$ $:\implies\sf\: -2u = 5 - 7$ $:\implies\sf\: -2u = -2$ $:\implies\sf\: u = \cancel\dfrac{-2}{-2}$ $:\implies\boxed{\sf{\pink{u\:=\:1}}}$ $\rule{200}2$ $:\implies\sf\: \dfrac{1}{y} = v$ $:\implies\sf\: \dfrac{1}{y} = 1$ $:\implies\sf\: 1 = y \times 1$ $:\implies\boxed{\sf{\pink{y\:=\:1}}}$ $\rule{200}2$ $:\implies\sf\:\dfrac{1}{x}=u$ $:\implies\sf\: \dfrac{1}{x}=1$ $:\implies\sf\: 1 = x \times 1$ $:\implies\boxed{\sf{\pink{x\:=\:1}}}$ Hence, Value of x & y is 1.