Systems of Equations and Inequalities Quick Check

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

A point is a solution to a system of equations if it satisfies all equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Tags

CCSS.6.EE.B.8

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane divided by a line, where one side of the line represents all the solutions.

Tags

CCSS.HSA.REI.D.12

Front

How do you determine if a point is a solution to an inequality?

Back

To determine if a point is a solution to an inequality, substitute the point's coordinates into the inequality. If the inequality holds true, the point is a solution.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Tags

CCSS.6.EE.B.8

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than', indicating that the value on the left is smaller than the value on the right.

Tags

CCSS.6.EE.B.8

Front

What is the significance of the solution (1, 3) in a system of equations?

Back

The solution (1, 3) indicates that when x=1 and y=3, both equations in the system are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you represent a real-world situation using a system of inequalities?

Back

A real-world situation can be represented using a system of inequalities by defining variables for the quantities involved and writing inequalities based on the constraints of the situation.

Front

What is the meaning of 'infinitely many solutions' in a system of equations?

Back

'Infinitely many solutions' means that there are countless points that satisfy all equations in the system, often occurring when the equations represent the same line.

Tags

CCSS.8.EE.C.8B