Solve the following pair of linear equations: | vedclass

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(D) Let $x = \frac{1}{a}$ and $y = \frac{1}{b}$.The equations become:$9x + 8y = 7$  --- $(1)$$2x - 3y = -8$ --- $(2)$Multiply $(1)$ by $3$ and $(2)$ b

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

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(D) Let $x = \frac{1}{a}$ and $y = \frac{1}{b}$.The equations become:$9x + 8y = 7$  --- $(1)$$2x - 3y = -8$ --- $(2)$Multiply $(1)$ by $3$ and $(2)$ by $8$ to eliminate $y$:$27x + 24y = 21$ --- $(3)$$16x - 24y = -64$ --- $(4)$Adding $(3)$ and $(4)$:$43x = -43 \implies x = -1$.Since $x = \frac{1}{a} = -1$,we get $a = -1$.Substitute $x = -1$ into $(2)$:$2(-1) - 3y = -8$$-2 - 3y = -8$$-3y = -6 \implies y = 2$.Since $y = \frac{1}{b} = 2$,we get $b = \frac{1}{2}$.Thus,$(a, b) = \left(-1, \frac{1}{2}\right)$.

Solve the following pair of linear equations: $\frac{9}{a} + \frac{8}{b} = 7$ and $\frac{2}{a} - \frac{3}{b} = -8$.

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