Algebra 1 Team Decathlon -- Event #2 Long Jump

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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How do you solve a system of equations using substitution?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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What is the difference between a system of equations and a system of inequalities?

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A system of equations consists of equations that are equal, while a system of inequalities consists of inequalities that define a range of possible solutions.

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What does it mean for a solution to be a feasible region in a system of inequalities?

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The feasible region is the set of all possible points that satisfy all inequalities in the system, often represented graphically.

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What is the graphical representation of a linear equation?

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A linear equation can be represented as a straight line on a graph, where each point on the line is a solution to the equation.

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How do you determine if a point is a solution to a system of equations?

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Substitute the point's coordinates into each equation. If the point satisfies all equations, it is a solution.

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What is the slope-intercept form of a linear equation?

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What does the slope of a line represent?

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The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

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How do you find the y-intercept of a linear equation?

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What is the significance of the x-intercept in a graph?

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