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Question

Fill in the blank:
The pair of equations x+2y=3 and 4x+4y=6 have ________.

A
Exactly one solution
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B
No solution
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C
Infinitely many solutions
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D
Two solutions
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Solution

The correct option is B Exactly one solution
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
x+2y=3 ----- (1)
4x+4y=6 ----- (2)
Comparing equations 1 and 2 with the general form of equation to write their co-efficient,
a1=1;a2=4;b1=2;b2=4;c1=3;c2=6
Compare the ratio, a1a2=b1b2=c1c2
14=24=36
If a1a2b1b2=c1c2, then the pair of linear equations has exactly one solution

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