Systems of Inequalities Practice

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What is a system of inequalities?

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

Tags

CCSS.HSA.REI.D.12

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How do you graph a system of inequalities?

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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.

Tags

CCSS.HSA.REI.D.12

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

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If a system of inequalities has no solution, it means that there is no ordered pair that satisfies all inequalities. This often occurs when the shaded regions do not overlap.

Tags

CCSS.HSA.REI.D.12

Front

What is the graphical representation of parallel lines in a system of equations?

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Parallel lines in a system of equations indicate that the system has no solution, as the lines never intersect.

Tags

CCSS.8.EE.C.8A

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

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To determine if an ordered pair is a solution, substitute the values of the ordered pair into each inequality. If the pair satisfies all inequalities, it is a solution.

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What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

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The solution is (2, 5).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean for a system of equations to be consistent?

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A system of equations is consistent if it has at least one solution, meaning the lines intersect at one or more points.

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CCSS.8.EE.C.8B

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What is the difference between a consistent and inconsistent system of equations?

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A consistent system has at least one solution (intersecting lines), while an inconsistent system has no solutions (parallel lines).

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CCSS.8.EE.C.8A

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

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

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How do you find the intersection point of two lines?

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To find the intersection point, solve the system of equations formed by the two lines simultaneously.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6