This is the basic and conceptual question from linear equations in two variables in which we have given two equations 2x-3y=7, (a+b)x-(a+b-3)y=4a+b and we have to find the value of a and b for which it has infinite solutions
Kindly solve the above equations
RS Aggarwal, Class 10, chapter 3D, question no 23
The equations are
2x−3y−7=0
(a+b)x−(a+b−3)y−(4a+b)=0
Here, a1​=2,b1​=−3,c1​=−7
a2​=a+b,b2​=−(a+b−3),c2​=−(4a+b)
The system of linear equations has infinite solutions
∴​a1​​/a2=b1​​/b2=c1/c2​​
⇒2/(a+b)=-3/−(a+b−3)​=-7/−(4a+b)​
⇒2/(a+b)=3/(a+b−3)​
⇒2a+2b−6=3a+3b
⇒b=−a−6
Again, we have
⇒3/(a+b−3)​=7/(4a+b)​
⇒12a+3b=7a+7b−21
⇒5a−4b=−21
Putting b=−a−6
⇒5a−4(−a−6)=−21⇒9a=−45
⇒a=−5
Putting  a=−5 in b=−a−6
⇒b=−(−5)−6⇒b=−1
⇒a=−5,b=−1