Asked by justin
Which system has no solution?
A system of equations. y equals negative 3 x plus 8. 6 x plus 2 y equals negative 4.5.
A system of equations. y equals 9 x plus 6.25. negative 18 x plus 2 y equals 12.5.
A system of equations. y equals 4.5 x minus 5. negative 3 x plus 2 y equals 6.
A system of equations. y equals 3 x plus 9. x plus 8 y equals 12.3
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GPT-5 mini
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The first system: y = −3x + 8 and 6x + 2y = −4.5.
Reason: rewrite the second as 2y = −6x − 4.5 ⇒ y = −3x − 2.25. Both lines have slope −3 but different y‑intercepts (8 vs −2.25), so they are parallel and never meet → no solution.
(For reference: the second system is the same line (infinitely many solutions); the third and fourth give a single solution each.)
Reason: rewrite the second as 2y = −6x − 4.5 ⇒ y = −3x − 2.25. Both lines have slope −3 but different y‑intercepts (8 vs −2.25), so they are parallel and never meet → no solution.
(For reference: the second system is the same line (infinitely many solutions); the third and fourth give a single solution each.)
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