Solving Systems of Equations by Graphing

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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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How do you solve a system of equations by graphing?

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To solve a system of equations by graphing, you graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

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What does the intersection point of two lines represent in a system of equations?

Back

The intersection point represents the solution to the system of equations, indicating the values of the variables that satisfy both equations.

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What is the significance of parallel lines in a system of equations?

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Parallel lines never intersect, which means there is no solution to the system of equations represented by those lines.

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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 change in y divided by the change in x (rise over run).

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How can you determine if two lines are parallel?

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Two lines are parallel if they have the same slope but different y-intercepts.

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What is the y-intercept of a line?

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The y-intercept is the point where the line crosses the y-axis, represented as (0, b) where b is the y-coordinate.

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What does it mean if two lines intersect at a single point?

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If two lines intersect at a single point, it means there is exactly one solution to the system of equations.

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What is the graphical representation of a solution to a system of equations?

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The graphical representation of a solution is the point where the graphs of the equations intersect on the coordinate plane.

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How can you check if your solution to a system of equations is correct?

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You can check if your solution is correct by substituting the values back into the original equations to see if they hold true.