Solve the following pair of linear equations: | vedclass

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(A) Let $x = \frac{1}{a}$ and $y = \frac{1}{b}$. The equations become:$8x - 9y = 1$  ---$(1)$$10x + 6y = 7$ ---$(2)$Multiply equation $(1)$ by $2$ and

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$(2, 3)$

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(A) Let $x = \frac{1}{a}$ and $y = \frac{1}{b}$. The equations become:$8x - 9y = 1$  ---$(1)$$10x + 6y = 7$ ---$(2)$Multiply equation $(1)$ by $2$ and equation $(2)$ by $3$ to eliminate $y$:$16x - 18y = 2$ ---$(3)$$30x + 18y = 21$ ---$(4)$Adding $(3)$ and $(4)$:$46x = 23 \implies x = \frac{23}{46} = \frac{1}{2}$.Since $x = \frac{1}{a}$,we have $a = 2$.Substitute $x = \frac{1}{2}$ into $(1)$:$8(\frac{1}{2}) - 9y = 1 \implies 4 - 9y = 1 \implies 9y = 3 \implies y = \frac{1}{3}$.Since $y = \frac{1}{b}$,we have $b = 3$.Thus,$(a, b) = (2, 3)$.

Solve the following pair of linear equations: $\frac{8}{a} - \frac{9}{b} = 1$ and $\frac{10}{a} + \frac{6}{b} = 7$.

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