Solving Systems by Graphing and Graphing Linear Inequalities

Front

What is a linear inequality?

Back

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

Front

What does the solution of a system of equations represent?

Back

The solution of a system of equations represents the point(s) where the graphs of the equations intersect, indicating the values of the variables that satisfy all equations in the system.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

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A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).

Front

What does it mean if a system of equations has no solution?

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A system of equations has no solution if the lines representing the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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A system of equations has infinitely many solutions if the lines representing the equations coincide, meaning they are the same line.

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How do you determine the number of solutions in a system of linear equations?

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To determine the number of solutions, analyze the slopes and y-intercepts of the lines: if they are the same, there are infinitely many solutions; if they are parallel, there is no solution; if they intersect, there is one solution.

Front

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

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Front

How do you convert a linear equation to slope-intercept form?

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Front

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

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