In the pair of equations a1x+b1y+c1=0 and a2x+b2y+c2=0,
a1a2=b1b2≠c1c2
Statement 1 : This is an inconsistent pair of linear equations.
Statement 2 : There exists infinitely many solutions.
Statement 3 : The lines representing these linese are parallel.
Which of the above statements is/are true?
S1 and S3
In the pair of equations a1x+b1y+c1=0 and a2x+b2y+c2=0,
if a1a2=b1b2≠c1c2, then the lines representing these equations are parallel.
Hence, there will be no solution and the pair of equations will be inconsistent.
∴ Statements 1 and 3 are correct.