Question

simultaneous equation

Answer 1

x = 2 and y = -3 is right answer.

Answer 2

Answer:

$\frac{4}{x} + \frac{3}{y} = 1 ⟹⓵\\ \frac{6}{x} - \frac{15}{y} = 8⟹⓶ \\ \\ Substituting \: \: a \: \: for \: \: \frac{1}{x} \: \: and \: \: b \: \: for \: \: \frac{1}{y} \\ \\ New \: \: Equation \: \: is: \\ 4a + 3b = 1⟹⓵ \\ 6a - 15b = 8⟹⓶ \\ \\ Multiply \: \: Equation \: \: ⓵ \: \: by \: \: 5 \\ (4a + 3b = 1) \times 5 \\ 20a + 15b = 5⟹⓵ \\ 6a - 15b = 8⟹⓶ \\ \\ Add \: \: the \: \: Two \: \: Equations : \\ 20a + 15b = 5 \\ 6a - 15b = 8 \\ - - - - - - - \\ 26a = 13 \\ a = \frac{ \cancel{ 13}_{ \: \: 1}}{ \cancel{ 26}_{ \: \: 2}} \\ \boxed{ \large a = \underline{ \underline{ \frac{1}{2} }}} \\ \\ 6a - 15b = 8 \\ ( _{3 \: \: }\cancel 6 \times \frac{1}{ \cancel 2 _{ \: \: 1} } ) - 15b = 8 \\ 3 - 15b = 8 \\ 3 - 8 = 15b \\ - 5 = 15b \\ \frac{_{ - 1 \: \: } \cancel{ - 5}}{_{3 \: \: } \cancel{ 15}} = b \\ \boxed{ \large{ \underline{ \underline{ \frac{ - 1}{3}}} = b}} \\ \\ a = \frac{1}{x} \\ \frac{1}{2} = \frac{1}{x} \\ \boxed{\large x = \underline{ \underline{ 2}}} \\ \\ b = \frac{1}{y} \\ \frac{ - 1}{3} = \frac{1}{y} \\ y = \frac{3}{ - 1} \\ \boxed{\large y = \underline{ \underline{ - 3}}}$