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Questions and Answers
Which classification describes the following system of equations? { x=5, y=6, -x-y+z=0 }
Which classification describes the following system of equations? { x=5, y=6, -x-y+z=0 }
Which classification describes the following system of equations? { 12x + 5y - 3z = 36, x - 2y + 4z = 3, 9x - 10y + 5z = 27 }
Which classification describes the following system of equations? { 12x + 5y - 3z = 36, x - 2y + 4z = 3, 9x - 10y + 5z = 27 }
What is the solution set of the quadratic inequality 6x^2 + 1?
What is the solution set of the quadratic inequality 6x^2 + 1?
There is no solution set
Study Notes
Quadratic Inequalities and Systems of Equations
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A consistent and independent system of equations has a unique solution, meaning that the equations do not interfere with each other.
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In the first system of equations:
- The equations are x=5, y=6, and -x-y+z=0.
- This system is classified as consistent and independent due to each equation providing distinct information leading to a single solution.
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In the second system:
- The equations are 12x - 5y - 3z=36, x - 2y + 4z=3, and 9x - 10y + 5z=27.
- This system is also consistent and independent, confirming that it has a unique solution where all equations intersect.
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For the quadratic inequality 6x^2 + 1, the analysis requires finding values of x where the expression remains non-negative (≥0).
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Quadratic inequalities can often be solved by interpreting them as equations, identifying critical points and testing intervals between those points to understand where the expression holds true.
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Test your knowledge on quadratic inequalities with these flashcards. Each card presents problems ranging from classification of systems of equations to solving quadratic inequalities. Perfect for reinforcing your understanding of the topic.
