Question

Solve the following pair of linear equations by the elimination method and the substitution method:::

1) 5x+8y=84
2x-3y=16​

Answer 1

ELIMINATION METHOD :

$5x+ 8y =84---(i)\\\\2x-3y=16---(ii)$

Multiply (i) equation by 2 and (ii) equation by 5 and then subtract (ii) from (i) :

$10x+16y=168\\10x-15y=80\\--------\\31y=88\\y=88/31$

Put value of y in (i) equation :

$5x+8(88/31)=84\\5x=84-704/31\\5x=(2604-704)/31\\5x =1900/31\\x=380/31$

SUBSTITUTION METHOD :

$5x+8y=84\\5x=84-8y\\x=(84-8y)/5---(i)\\2x-3y=16---(ii)$

Put value of (i) in (ii) :

$2[(84-8y)/5]-3y=16\\(168-16y)/5-3y=16\\168-16y-15y=16*5\\168-31y=80\\31y=168-80\\y=88/31$

Put value of y in (i) equation :

$x=\frac{[84-(88/31)8]}{5}\\\\x=\frac{2604-704}{31*5}\\ \\x=\frac{1900}{31*5}\\ \\x=380/31$