#5.1 Solving Systems of Linear Equations by Graphing

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear equations in the same variable.

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What is a solution to a system of linear equations?

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A solution to a system of linear equations is an ordered pair that satisfies both equations.

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How can you determine if an ordered pair is a solution to a system of linear equations?

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You can determine if an ordered pair is a solution by substituting the values into both equations and checking if both equations are true.

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What does it mean if two lines intersect on a graph?

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If two lines intersect on a graph, it means that there is a unique solution to the system of equations represented by those lines.

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What does it mean if two lines are parallel on a graph?

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If two lines are parallel, it means that there is no solution to the system of equations, as the lines will never intersect.

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What does it mean if two lines coincide on a graph?

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If two lines coincide, it means that there are infinitely many solutions to the system of equations, as the lines are the same.

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How do you graph a linear equation?

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To graph a linear equation, you can find two or more points that satisfy the equation and then connect them with a straight line.

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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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What is the y-intercept of a line?

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The y-intercept of a line is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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What is the standard form of a linear equation?

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The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A is non-negative.