Question

Examine the consistency of the system of equations in: x + 3y = 5 2x + 6y = 8

Answer 1

Answer:

no solution

Step-by-step explanation:

x = 3y + 5

2•(3y+5) - 6y = 8

0 = -2 =>  NO solution

Answer 2

Answer:

System is not consistent.

Step-by-step explanation:

x + 3y = 5  

2x + 6y= 8

We can write these equation as follows:

x + 3y - 5 = 0

2x + 6y - 8 = 0

Folowing is the general equation in two variable:

$a_1x+b_1y+c_1=0\\a_2x+b_2y+c_2=0$

For checking of the  system of equation:(use the following formula).

$\dfrac{a_1}{a_2}\neq \dfrac{b_1}{b_2}$

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$

$a_1=1\ ,b_1=3\ ,c_1=-5\\a_2=2\ ,b_2=6\ ,c_2=-8$

We get from given equation:

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}$

$\dfrac{1}{2}=\dfrac{3}{6}\neq\dfrac{-5}{-8}$

$\dfrac{1}{2}=\dfrac{1}{2}\neq\dfrac{-5}{-8}$

Hence system is not consistent.