For what value of a and b, the following system of equations have an infinite number of solutions.$2x+3y=7; (a-b)x+(a+b)y=3a+b-2$

Given: System of the equations $2x+3y=7;\ (a-b)x+(a+b)y=3a+b-2$

To do: To find the value of $a$ and $b$.

Solution:

$2x+3y=7$

$(a−b)x+(a+b)y=3a+b−2$

$\because$ It has infinitely many solutions.
 
$\therefore \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
​
$\frac{2}{a−b}=\frac{3}{a+b}=\frac{7}{3a+b−2}$
​
From $( i)$ and $( ii)$

$\frac{3}{a+b}=\frac{7}{3a+b−2}$

$7a+7b=9a+3b−6$

$\Rightarrow 2a−4b=6$

$\Rightarrow a−2b=3$

$\Rightarrow 5b−2b=3$

$\Rightarrow 3b=3\Rightarrow b=1$

$\therefore  a=5\times 1=5$.
 

Updated on: 10-Oct-2022

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