Lesson Objectives Show
How to Graph a System of Linear InequalitiesWe previously learned how to graph a linear inequality in two variables. Let's review this procedure and then move into solving systems of linear inequalities. Graphing a Linear Inequality in Two Variables
Graphing a System of Linear Inequalities
When we graph a system of linear inequalities in two variables, we graph each inequality and look for the overlap of the graphs. This overlap is the solution region for the system since it is the area of the coordinate plane that satisfies both inequalities of the system. Let's look at a few examples. Systems of Linear Inequalities with No Solution In some cases, we will see a system of linear inequalities with no solution. This will occur when the boundary lines are parallel and there is no overlap between the two graphs. Let's take a look at an example.
Skills Check:Example #1 Determine which system matches the graph. Please choose the best answer.
A $$2x + 5y > 7$$ $$x - 3y ≤ -2$$ B $$x - 2y > 4$$ $$2x - y ≤ -1$$ C $$2x + 7y < -2$$ $$4x + 5y ≥ -3$$ D $$3x + y < 1$$ $$x - y ≥ -1$$ E $$3x + 5y > 2$$ $$3x + 4y ≤ 7$$ Example #2 Determine which system matches the graph. Please choose the best answer. A $$x - 3y < -6$$ $$2x + 3y < 6$$ B $$x + 3y < 6$$ $$-x - 3y > 5$$ C $$2x - 7y > -2$$ $$4x + 5y > 8$$ D $$3x + 9y < 1$$ $$x - 2y < 4$$ E $$5x + 3y < -6$$ $$x + 3y < 6$$ Example #3 Determine which system matches the graph. Please choose the best answer. A $$5x - 3y > 7$$ $$x + 4y ≤ 2$$ B $$2x + 5y > 7$$ $$13x - 9y ≤ 7$$ C $$x + y > -2$$ $$4x - y ≤ -3$$ D $$2x - 5y < -9$$ $$x - 3y ≥ 8$$ E $$4x - 7y ≤ -1$$ $$x + 13y > 7$$ Congrats, Your Score is 100% Better Luck Next Time, Your Score is % Try again?
How do you graph and shade a system of linear inequalities?There are three steps:. Rearrange the equation so "y" is on the left and everything else on the right.. Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>). Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).. Why do you shade the graph of a linear inequality?We shade below (not above) because y is less than (or equal to) the other side of the inequality. We draw a solid line (not dashed) because we're dealing with an "or equal to" inequality. The solid line indicates that points on the line are solutions to the inequality.
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