Question

Find whether the following pair of linear equations is consistent or inconsistent:

x + 2y = 4, 3x + 6y = 12​

Answer 1

Answer:

x+2y/4,3x+6y=12=3x+x=4x

Answer 2

Given

The given system of equations are

x+2y =4

3x+6y =12

To find:

We have to find whether the given equations are consistent or inconsistent

Solution:

Let us compare given equations with

$a_{1}x+b_{1}y+c_1=0$

$a_{2}x+b_{2}y+c_2=0$

then we get  $a_1=1$ , $b_1=2$ ,$c_1=-4$

                     $a_2=3$ , $b_2=6$ ,$c_2=-12$

Compute,

$\frac{a_1}{a_2}=\frac{1}{3}$

$\frac{b_1}{b_2} =\frac{2}{6}=\frac{1}{3}$

$\frac{c_1}{c_2}=\frac{-4}{-12}=\frac{1}{3}$

Here  $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Hence the given equations are CONSISTENT and DEPENDENT