This question is taken from linear equations in two variables in which we have given two equations 2x+3y=7, (k-1)x+(k+2)y=3k and we have to find the value of k for which these equations have indefinitely many solutions.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 3F, question no 2
2x+3y=7
(k−1)x+(k+2)y=3k
These given equations are in the form:
a1​x+b1​y+c1​=0 and
a2​x+b2​y+c2​=0
Where
a1​=2, b1​=3 and c1​=7
a2​=(k−1), b2​=(k+2) and c2​=3k
a1/​a1​2=2/(k−1)​, b1/b2​​=3/(k+2)​,c1/c2​​=7/3k​
Which shows:
a1/​a2=b1/b2=c1/​c2​​
System has infinitely many solutions.
Now, Find the value of k
2/(k−1)=3/(k+2)=7/3k​
2/(k−1)=3/(k+2)
3(k−1)=2(k+2)
which implies, k=7
The value of k is 7.