solve b

5a-3/a =3

7b-1=a-21

asked by guest
on Mar 28, 2025 at 12:29 pm



You asked:

Solve the equations 5a−3a=37b−1=a−21\begin{aligned}5 a - \frac{3}{a} &= 3\\7 b - 1 &= a - 21\end{aligned} for the unknown bb.

MathBot Answer:

The system of equations has 22 solutions.

a=310−6910,b=−19770−6970a = \frac{3}{10} - \frac{\sqrt{69}}{10}, b = - \frac{197}{70} - \frac{\sqrt{69}}{70}a=310+6910,b=−19770+6970a = \frac{3}{10} + \frac{\sqrt{69}}{10}, b = - \frac{197}{70} + \frac{\sqrt{69}}{70}

Solve 5a−3a=35 a - \frac{3}{a} = 3 for aa. a=310−6910,a=310+6910a = \frac{3}{10} - \frac{\sqrt{69}}{10}, a = \frac{3}{10} + \frac{\sqrt{69}}{10}Substitute 310−6910\frac{3}{10} - \frac{\sqrt{69}}{10} for aa in 7b−1=a−217 b - 1 = a - 21 and solve.7b−1=−20710−69107b=−19710−6910b=−19770−6970\begin{aligned}7 b - 1 &= - \frac{207}{10} - \frac{\sqrt{69}}{10}\\7 b &= - \frac{197}{10} - \frac{\sqrt{69}}{10}\\b &= - \frac{197}{70} - \frac{\sqrt{69}}{70}\end{aligned}This yields the following solution. a=310−6910, b=−19770−6970\begin{aligned}a = \frac{3}{10} - \frac{\sqrt{69}}{10},\,b = - \frac{197}{70} - \frac{\sqrt{69}}{70}\end{aligned}Substitute 310−6910\frac{3}{10} - \frac{\sqrt{69}}{10} for aa in 7b−1=a−217 b - 1 = a - 21 and simplify. 7b−1=a−217b−1=(310−6910)−21b=−19770−6970\begin{aligned}7 b - 1 &= a - 21 \\ 7 b - 1 &= \left(\frac{3}{10} - \frac{\sqrt{69}}{10}\right) - 21 \\ b &= - \frac{197}{70} - \frac{\sqrt{69}}{70} \end{aligned}Substitute −19770−6970- \frac{197}{70} - \frac{\sqrt{69}}{70} into 7b−1=a−217 b - 1 = a - 21 to solve for aa. −20710−6910=a−21−a=−310+6910a=310−6910\begin{aligned}- \frac{207}{10} - \frac{\sqrt{69}}{10} &= a - 21\\- a &= - \frac{3}{10} + \frac{\sqrt{69}}{10}\\a &= \frac{3}{10} - \frac{\sqrt{69}}{10}\end{aligned}This yields the following solutions. a=310−6910, b=−19770−6970\begin{aligned}a = \frac{3}{10} - \frac{\sqrt{69}}{10},\,b = - \frac{197}{70} - \frac{\sqrt{69}}{70}\end{aligned}Substitute 310+6910\frac{3}{10} + \frac{\sqrt{69}}{10} for aa in 7b−1=a−217 b - 1 = a - 21 and solve.7b−1=−20710+69107b=−19710+6910b=−19770+6970\begin{aligned}7 b - 1 &= - \frac{207}{10} + \frac{\sqrt{69}}{10}\\7 b &= - \frac{197}{10} + \frac{\sqrt{69}}{10}\\b &= - \frac{197}{70} + \frac{\sqrt{69}}{70}\end{aligned}This yields the following solution. a=310+6910, b=−19770+6970\begin{aligned}a = \frac{3}{10} + \frac{\sqrt{69}}{10},\,b = - \frac{197}{70} + \frac{\sqrt{69}}{70}\end{aligned}

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