The correct option is C x+2y=5;2x+4y=15
A pair of linear equations in two variables is said to be inconsistent when:
a1a2=b1b2≠c1c2
Consider the equations given in option A.
2x+3y=15
4x+7y=11
Here, a1=2, b1=3 and c1=−15
Also, a2=4, b2=7 and c2=−11
Here, 24≠37
⇒a1a2≠b1b2
∴ Equations in option A have unique solution and are consistent.
Consider equations given in option B.
48=12=1224⇒12=12=12
⇒a1a2=b1b2=c1c2
∴ Equations in option B have infinite solutions and are consistent.
Consider equations given in option C.
12=24≠515
⇒a1a2=b1b2≠c1c2
∴ Equations in option C have no solution and are inconsistent.
Consider equations given in option D.
32≠115
⇒a1a2≠b1b2
∴ Equations in option D have a unique solution and are consistent.