Question

for what value of a the system of linear equations 2x + 3y = 7 and ( a -1 )x + (a + 1)y = 3a + 1 represent parallel lines?​

Answer 1

$\textsf{Given:}$

$\textsf{2x+3y-7=0\;\;\&\;\;( a -1 )x + (a + 1)y -(3a + 1)=0}$

$\textsf{We know that,}$

$\textsf{Equations of parallel line differ only by constant term}$

$\textsf{That is,their corresponding coefficients are proportional}$

$\implies\mathsf{\frac{2}{a-1}=\frac{3}{a+1}}$

$\implies\mathsf{2(a+1)=3(a-1)}$

$\implies\mathsf{2a+2=3a-3}$

$\implies\mathsf{a=2+3}$

$\implies\mathsf{a=5}$

$\therefore\textsf{The required value of a is 5}$

Answer 2

Answer:

Given:

\textsf{2x+3y-7=0\;\;\&\;\;( a -1 )x + (a + 1)y -(3a + 1)=0}2x+3y-7=0&( a -1 )x + (a + 1)y -(3a + 1)=0

\textsf{We know that,}We know that,

\textsf{Equations of parallel line differ only by constant term}Equations of parallel line differ only by constant term

\textsf{That is,their corresponding coefficients are proportional}That is,their corresponding coefficients are proportional

\implies\mathsf{\frac{2}{a-1}=\frac{3}{a+1}}⟹

a−1

2

=

a+1

3

\implies\mathsf{2(a+1)=3(a-1)}⟹2(a+1)=3(a−1)

\implies\mathsf{2a+2=3a-3}⟹2a+2=3a−3

\implies\mathsf{a=2+3}⟹a=2+3

\implies\mathsf{a=5}⟹a=5

\therefore\textsf{The required value of a is 5}∴The required value of a is 5