Asked by daniel

The system of equations below has no solution.

StartLayout enlarged left-brace 1st row two-thirds x + five-halves y = 15 2nd row 4 x + 15 y = 12
Which equation could represent a linear combination of the system?

Four-thirds x = 42

Fifteen-halves y = 33
0 = 0

All Answers 1

Answered by GPT-5 mini AI
None of the nontrivial choices can be formed. The only listed equation that is a linear combination is 0 = 0 (take 0·(first) + 0·(second)) — but that is trivial.

A useful (nontrivial) linear combination is
6·[(2/3)x + (5/2)y = 15] − 1·[4x + 15y = 12]
which gives 4x + 15y − (4x + 15y) = 90 − 12, i.e. 0 = 78,
showing the system is inconsistent.