The pair of linear equation is consistent and dependent .
A linear equation is an equation which has the highest power of variable as 1 , it is also called as a one degree equation.
a pair of linear equation is given
a₁x +b₁y +c₁
a₂x +b₂y +c₂
The equations are
x - 3y = 5
2x + 6y = 8
a₁ = 1
b₁ = -3
c₁ = -5
a₂ = 2
b₂ = 6
c₂ = -8
if
[tex]\rm \dfrac{a_1}{a_2} \ne \dfrac{b_1}{b_2}\\[/tex]
then the equation has a unique solution and is consistent or dependent
[tex]\rm \dfrac{a_1}{a_2} = \dfrac{1}{2}\\\\\\ \dfrac{b_1}{b_2} = \dfrac{-3}{6} = \dfrac{-1}{2}[/tex]
as
[tex]\rm \dfrac{a_1}{a_2} \ne \dfrac{b_1}{b_2}\\[/tex]
Therefore the pair of linear equation is consistent and dependent .
The equations are
x - 3y = 5
2x + 6y = 8
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