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:
a1x+b1y+c1=0 and
a2x+b2y+c2=0
Where
a1=2, b1=3 and c1=7
a2=(k−1), b2=(k+2) and c2=3k
a1/a12=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.