Solve the equations by elimination method.$8a+20b=1$
$9a+18b=1$

Given: Equations :$8a+20b=1$ and $9a+18b=1$

To do: To solve the equations by elimination method.

Solutions:

Given equations are:

$8a+20b=1$ ......... $( i)$

$9a+18b=1$ ..........$( ii)$

On multiplying the $( i)$ by $9$ and $( ii)$ by $8$

$72a+180b=9$ ........ $( iii)$

$72a+144b=8$ ....... $( iv)$

On subtracting $( iv)$ from $( iii)$

$72a+180b-72a-144b=9-8$

$\Rightarrow 36b=1$

$\Rightarrow b=\frac{1}{36}$, On putting this value in $( i)$

$8a+20\times\frac{1}{36}=1$

$\Rightarrow 8a+\frac{20}{36}=1$

$\Rightarrow 8a+\frac{5}{9}=1$

$\Rightarrow 8a=1-\frac{5}{9}$

$\Rightarrow 8a=\frac{9-5}{9}$

$\Rightarrow 8a=\frac{4}{9}$

$\Rightarrow a=\frac{4}{9}\times\frac{1}{8}$

$\Rightarrow a=\frac{1}{18}$

Thus, $a=\frac{1}{18}$ and $b=\frac{1}{36}$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

45 Views

Kickstart Your Career

Get certified by completing the course

Get Started