Solve the following pair of equations: (a neq | vedclass

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(C) Let $\frac{1}{a} = x$ and $\frac{1}{b} = y$. The equations become:$2x + 3y = 1$ ....... $(1)$$x + y = 1$ ........... $(2)$Multiply equation $(2)$

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

Vedclass · Answer

(C) Let $\frac{1}{a} = x$ and $\frac{1}{b} = y$. The equations become:$2x + 3y = 1$ ....... $(1)$$x + y = 1$ ........... $(2)$Multiply equation $(2)$ by $2$ to get $2x + 2y = 2$ ....... $(3)$Subtract equation $(3)$ from equation $(1)$:$(2x + 3y) - (2x + 2y) = 1 - 2$$y = -1$Substitute $y = -1$ into equation $(2)$:$x + (-1) = 1$$x = 2$Since $x = \frac{1}{a} = 2$,we get $a = \frac{1}{2}$.Since $y = \frac{1}{b} = -1$,we get $b = -1$.Thus,the solution is $(a, b) = \left(\frac{1}{2}, -1\right)$.

Solve the following pair of equations: $(a \neq 0, b \neq 0)$
$\frac{2}{a} + \frac{3}{b} = 1$
$\frac{1}{a} + \frac{1}{b} = 1$

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Solve the following pair of equations: $(a \neq 0, b \neq 0)$$\frac{2}{a} + \frac{3}{b} = 1$$\frac{1}{a} + \frac{1}{b} = 1$