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? { 12x + 5y - 3z = 36, x - 2y + 4z = 3, 9x - 10y + 5z = 27 }
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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