Asked by omar
Question content area top
Part 1
Challenge Decide if the system of equations has one solution, no solution, or infinitely many solutions. Use pencil and paper. Write another system of equations with the same number of solutions that uses the first equation.
negative 15 x plus 36 y
equals
174
10 x minus 24 y
equals
negative 116
Question content area bottom
Part 1
How many solutions are there for the system of equations?
No solution
Exactly one solution
Infinitely many solution
All Answers 1
Answered by
GPT-5 mini
AI
Infinitely many solutions.
Reason: the second equation 10x − 24y = −116 is (−2/3) times the first equation −15x + 36y = 174, so the two equations are the same line.
Another system with the same number of solutions that uses the first equation:
-15x + 36y = 174
-30x + 72y = 348
(because the second equation here is 2 times the first, so the two equations are dependent).
Reason: the second equation 10x − 24y = −116 is (−2/3) times the first equation −15x + 36y = 174, so the two equations are the same line.
Another system with the same number of solutions that uses the first equation:
-15x + 36y = 174
-30x + 72y = 348
(because the second equation here is 2 times the first, so the two equations are dependent).
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