Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.2, x, plus, 3, y, equals, minus, 12x+3y=−1minus, 2, x, minus, 3, y, equals, 1−2x−3y=1
Question
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.2, x, plus, 3, y, equals, minus, 12x+3y=−1minus, 2, x, minus, 3, y, equals, 1−2x−3y=1
Solution
The system of equations is:
- 2x + 3y = -1
- -2x - 3y = 1
To determine if the system has no solutions, infinitely many solutions, or exactly one solution, we can add the two equations together:
(2x + 3y) + (-2x - 3y) = -1 + 1
This simplifies to 0 = 0, which is always true. This means that the system of equations has infinitely many solutions.
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