An important and exam oriented question from linear equations in two variables in which we have given two equations 10x+5y-(k-5)=0, 2x+10y-k=0 and we have been asked to find the value of k for which the given equations have indefinitely many solutions
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 3F, question no 3
10x+5y−(k−5)=0and
20x+10y−k=0
These given equations are in the form:
a1​x+b1​y+c1​=0 and
a2​x+b2​y+c2​=0
Where
a1​=10,b1​=5 and c1​=−(k−5)
a2​=20,b2​=10 and c2​=−k
System has infinitely many solutions.
10/20​=5/10​=−(k−5)/-k​=(k−5)/k​
5k=10k−50
or k=10
The value of k is 10.