Solving Systems of Equations Graphically

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What is a system of equations?

Back

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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What does it mean to solve a system of equations graphically?

Back

Solving a system of equations graphically means finding the point(s) where the graphs of the equations intersect, which represents the solution(s) to the system.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, typically written as (x, y).

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How do you identify the solution of a system of equations from a graph?

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The solution is identified as the point where the graphs of the equations intersect.

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What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the values of the variables that satisfy all equations in the system simultaneously.

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What does it mean if two lines are parallel in a system of equations?

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If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

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What does it mean if two lines coincide in a system of equations?

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.

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

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To determine if a point is a solution, substitute the x and y values of the point into each equation. If both equations are satisfied, the point is a solution.

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What is the graphical representation of the equation y = mx + b?

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The equation y = mx + b represents a straight line in a graph, where m is the slope and b is the y-intercept.

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).