Solve the following pairs of linear equations | vedclass

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Question

(C) Let $x = \frac{1}{a}$ and $y = \frac{1}{b}$.The equations become:$5x - 6y = 3$  --- $(1)$$x + 4y = 11$  --- $(2)$From equation $(2)$,$x = 11 - 4y$

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$\left(\frac{1}{3}, \frac{1}{2}\right)$

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(C) Let $x = \frac{1}{a}$ and $y = \frac{1}{b}$.The equations become:$5x - 6y = 3$  --- $(1)$$x + 4y = 11$  --- $(2)$From equation $(2)$,$x = 11 - 4y$.Substitute $x$ in equation $(1)$:$5(11 - 4y) - 6y = 3$$55 - 20y - 6y = 3$$55 - 26y = 3$$26y = 52$$y = 2$.Since $y = \frac{1}{b} = 2$,then $b = \frac{1}{2}$.Substitute $y = 2$ in $x = 11 - 4y$:$x = 11 - 4(2) = 11 - 8 = 3$.Since $x = \frac{1}{a} = 3$,then $a = \frac{1}{3}$.Thus,$(a, b) = \left(\frac{1}{3}, \frac{1}{2}\right)$.

Solve the following pairs of linear equations: $\frac{5}{a} - \frac{6}{b} = 3$ and $\frac{1}{a} + \frac{4}{b} = 11$.

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