Question

Using cross multiplication method find 1/x+1/y=7,2/x+3/y=17

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{\dfrac{1}{x}+\dfrac{1}{y}=7}$

$\mathsf{\dfrac{2}{x}+\dfrac{3}{y}=17}$

$\underline{\textbf{To find:}}$

$\textsf{Solution of the given simultaneous equations}$

$\underline{\textbf{Solution:}}$

$\textsf{The given equations can be written as}$

$\mathsf{\dfrac{1}{x}+\dfrac{1}{y}-7=0}$

$\mathsf{2\left(\dfrac{1}{x}\right)+3\left(\dfrac{1}{y}\right)-17=0}$

$\textsf{Using Cross multiplication rule,}$

$\mathsf{\dfrac{\dfrac{1}{x}}{-17+21}=\dfrac{\dfrac{1}{y}}{-14+17}=\dfrac{1}{3-2}}$

$\mathsf{\dfrac{\dfrac{1}{x}}{4}=\dfrac{\dfrac{1}{y}}{3}=\dfrac{1}{1}}$

$\mathsf{\dfrac{\dfrac{1}{x}}{4}=\dfrac{1}{1}}$

$\mathsf{\dfrac{1}{x}=4}$

$\implies\boxed{\mathsf{x=\dfrac{1}{4}}}$

$\mathsf{and}$

$\mathsf{\dfrac{\dfrac{1}{y}}{3}=\dfrac{1}{1}}$

$\mathsf{\dfrac{1}{y}=3}$

$\implies\boxed{\mathsf{y=\dfrac{1}{3}}}$

$\therefore\mathsf{Solution\;is\;x=\dfrac{1}{4}\;and\;y=\dfrac{1}{3}}$

$\underline{\textbf{Find more:}}$

2x+y=35;3x+4y=65 solve by using cross multiplication method

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Solve each of the following systems of equations by the method of cross-multiplication:

ax + by = a²

bx + ay = b²

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Solve each of the following systems of equations by the method of cross-multiplication:

a²x+b²y=c²b²x+a²y=a²

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Answer 2

Step-by-step explanation:

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