Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you graph a linear inequality?

Back

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

Front

What does the solution of a system of inequalities represent?

Back

The solution of a system of inequalities represents all the points that satisfy all inequalities in the system, often visualized as a shaded region on a graph.

Front

What is the difference between 'no solution' and 'infinite solutions' in a system of inequalities?

Back

'No solution' means there are no points that satisfy all inequalities, while 'infinite solutions' means there are countless points that satisfy all inequalities.

Front

What does the inequality y < 2x + 1 represent graphically?

Back

It represents all points below the line y = 2x + 1, not including the line itself.

Front

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

Back

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

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line indicates the limit of the solution set. Points on the line are included if the inequality is ≤ or ≥, and excluded if it is < or >.

Front

What does the inequality x ≥ -1 mean?

Back

It means all values of x that are greater than or equal to -1, including -1 itself.

Front

How can you tell if a system of inequalities has no solution?

Back

If the graphs of the inequalities do not intersect or overlap, the system has no solution.

Front

What does the inequality y > -x + 2 represent?

Back

It represents all points above the line y = -x + 2, not including the line itself.