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Consistency of Linear System of Equations

Solve the fol...

Question

Solve the following pair of equations
$\frac{4}{x} + 3 y = 8; \frac{6}{x} - 4 y = - 5$

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Solution

$\begin{matrix} \Rightarrow \frac{4}{x} + 3 y = 8........ (1) \Rightarrow \frac{6}{x} - 4 y = - 5 \Rightarrow - 4 y = \frac{(- 5 - 6)}{x} \Rightarrow y = \frac{(5 x + 6)}{4 x} . . . . . . . . . . (2) n o w, s u b s t i t u t i n g v a l u e o f y i n e q u a t i o n (1) \Rightarrow \frac{4}{x} + \frac{3 (5 x + 6)}{4 x} = 8 \Rightarrow \frac{(16 + 15 x + 18)}{4 x} = 8 \Rightarrow 34 + 15 x = 32 x \Rightarrow 34 = 17 x \Rightarrow x = 2 n o w, s u b s t i u t i n g x i n e q u a t i o n (2) \Rightarrow y = \frac{(5 x + 6)}{4 x} \Rightarrow y = (\frac{10 + 6}{8}) \Rightarrow y = \frac{16}{8} \Rightarrow y = 2 t h e r e f o r e, x = y = 2 \end{matrix}$

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Similar questions

\begin{matrix} \frac{4}{x} + 3 y = 8 \frac{6}{x} - 4 y = - 5 \end{matrix}

Solve the following systems of equations:

$\frac{4}{x} + 3 y = 8$

$\frac{6}{x} - 4 y = - 5$

Q. Solve the following pair of equations by reducing them to a pair of linear equations:

\frac{4}{x} + 3 y = 14, \frac{3}{x} - 4 y = 23

Q. Question 1 (iii)
Solve the following pairs of equations by reducing them to a pair of linear equations:

\frac{4}{x} + 3 y = 14

\frac{3}{x} - 4 y = 23

Solve the following pair of equations:

3 - (x - 5) = y + 2

2 (x + y) = 4 - 3 y

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Consistency of Linear System of Equations

Standard XII Mathematics

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