Systems of Equations

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What is a system of equations?

Back

A set of two or more equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

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It means that the point satisfies all equations in the system.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the graphical representation of a system of equations?

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The graphical representation consists of lines or curves that intersect at points.

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CCSS.8.EE.C.8B

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What does it indicate if two lines in a system of equations are parallel?

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It indicates that the system has no solution.

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CCSS.8.EE.C.8B

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How can you determine the number of solutions in a system of equations?

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By analyzing the graphs of the equations: one intersection point indicates one solution, no intersection indicates no solution, and infinite intersections indicate infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

What is an ordered pair in the context of systems of equations?

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An ordered pair is a pair of numbers (x, y) that represents a point on the coordinate plane.

Tags

CCSS.8.EE.C.8A

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What is the solution of a system of equations?

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The solution is the ordered pair that satisfies all equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Tags

CCSS.8.EE.C.8A

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What is the substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6