for what value of k the following pair of linear equations has infinitely many solutions 10x + 5y -(k-5)=0
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Answer : 10
Step-by-step explanation : 10x+5y−(k−5)=0and
20x+10y−k=0
These given equations are in the form:
a
1
x+b
1
y+c
1
=0 and
a
2
x+b
2
y+c
2
=0
Where
a
1
=10,b
1
=5 and c
1
=−(k−5)
a
2
=20,b
2
=10 and c
2
=−k
System has infinitely many solutions.
20
10
=
10
5
=
−k
−(k−5)
=
k
k−5
5k=10k−50
or k=10
The value of k is 10.
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