Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.5, x, plus, y, equals, minus, 35x+y=−3minus, 5, x, minus, y, equals, 3−5x−y=3AnswerMultiple Choice AnswersOne SolutionOne SolutionNo SolutionsNo SolutionsInfinitely Many SolutionsInfinitely Many Solutions
Question
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.5, x, plus, y, equals, minus, 35x+y=−3minus, 5, x, minus, y, equals, 3−5x−y=3AnswerMultiple Choice AnswersOne SolutionOne SolutionNo SolutionsNo SolutionsInfinitely Many SolutionsInfinitely Many Solutions
Solution
To determine the number of solutions for the given system of equations, we can use the method of elimination.
First, let's write the system of equations in standard form:
5x + y = -35 (Equation 1) -5x - y = 3 (Equation 2)
To eliminate the y variable, we can add Equation 1 and Equation 2 together:
(5x + y) + (-5x - y) = -35 + 3 0 = -32
This equation simplifies to 0 = -32, which is not true.
Since the equation is inconsistent (0 ≠ -32), the system of equations has no solutions.
Therefore, the correct answer is: No Solutions.
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