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Question

Solve the equation: 5x+y=1 and 5xy=0 and then identify the system of equation

A
Consistent
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B
Inconsistent
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C
Dependent
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D
All the above
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Solution

The correct option is C Dependent
The general form for a pair of linear equations in two variables x and y is
a1x+b1y+c1=0 and
a2x+b2y+c2=0
5x+y=1 ----- (1)
5xy=0----- (2)
Comparing equations 1 and 2 with the general form of equation to write their co-efficient,
a1=5;a2=5;b1=1;b2=1;c1=1;c2=0
Compare the ratio, a1a2=b1b2=c1c2
55=11=10
If a1a2=b1b2c1c2, then the pair of linear equations has exactly one solution.
So, 1=1=1 it said to be consistent.

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