Question

Is the system consistent or inconsistent? 2x + 3y = 5 and 4x + 6y = 19
consistent
inconsistent

Answer 1

If you look at the two equations you can see that for the left hand side, the second is simply double the first! As in, 4x+6y is double 2x+3y. So, if the system were consistent it would follow that the right hand side would be double, but 19 isn't double 5, so the system must be inconsistent!

Answer 2

thanks

Answer 3

The system is inconsistent since there is no solution for the system.
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Ideas: 2x+3y = 5 is equivalent to 4x+6y = 10. So, 4x+6y = 19 at the same time is impossible.

Answer 4

rule for inconsistency
a1/a2=b1/b2 but not =c1/c2.
here a1=2 a2=4 b1=3 b2=6 c1=5 c2=19

so the sytem in inconsistent n indeterminant

Answer 5

no solution