Question

Show that the system of equations: 3x + 5y = 8 and 6x + 10y = 10 is inconsistent.

Answer 1

$\huge\boxed{\underline{\underline{\green{Solution}}}} </p><p>$

TO PROVE

The system of equations: 3x + 5y = 8 and 6x + 10y = 10 is inconsistent.

FORMULA TO BE IMPLEMENTED :

A pair of Straight Lines

$\displaystyle \sf{} a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

are said to be inconsistent if

$\displaystyle \sf{} \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \: \frac{c_1}{c_2}$

CALCULATION :

Given pair of linear equations

$\sf{}3x +5y = 8 \: \: and \: \: 6x + 10y =10$

Comparing with

$\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

We get

$\displaystyle \sf{}a_1 = 3 , b_1 = 5, c_1= - 8 \: and \: a_2 = 6 , b_2 =10 , c_2= - 10$

Now

$\displaystyle \sf{} \frac{a_1}{a_2} = \frac{3}{6} = \frac{1}{2}$

$\displaystyle \sf{} \frac{b_1}{b_2} = \frac{5}{10} = \frac{1}{2}$

$\displaystyle \sf{} \frac{c_1}{c_2} = \frac{8}{10} = \frac{4}{5}$

$\therefore \: \: \displaystyle \sf{} \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \: \frac{c_1}{c_2}$

Hence The system of equations 3x + 5y = 8 and 6x + 10y = 10 is inconsistent

Hence proved

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

The product of two successive multiples of 5 is 300. What are the values of these multiples

https://brainly.in/question/26660243