Alg 1H: Solving Systems of Inequalities Flashcard

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 system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the region that satisfies the inequality. The solution to the system is where the shaded regions overlap.

Front

What does the inequality x + y < 10 represent?

Back

It represents all the points (x, y) in the coordinate plane where the sum of x and y is less than 10.

Front

What does the inequality 2x + 3y ≥ 20 represent?

Back

It represents all the points (x, y) in the coordinate plane where the weighted sum of x and y is at least 20.

Front

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

Back

The boundary line represents the points where the inequality changes from true to false. If the inequality is strict (e.g., < or >), the line is dashed; if it is inclusive (e.g., ≤ or ≥), the line is solid.

Front

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

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

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

Back

It means there is no point that satisfies all inequalities in the system, often because the shaded regions do not overlap.

Front

What does it mean if a system of inequalities has infinite solutions?

Back

It means there are infinitely many points that satisfy all inequalities, typically when the inequalities represent the same line or overlapping regions.

Front

What is the graphical representation of y ≤ 2x - 1?

Back

It is a solid line with a slope of 2 and a y-intercept of -1, with the region below the line shaded.

Front

What is the graphical representation of y > -2x + 3?

Back

It is a dashed line with a slope of -2 and a y-intercept of 3, with the region above the line shaded.