8.EE.8 Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean for a system of equations to have one solution?

Back

It means that the lines represented by the equations intersect at exactly one point.

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CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

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

Tags

CCSS.8.EE.C.8A

Front

How do you solve a system of equations by substitution?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve a system of equations by elimination?

Back

1. Align the equations. 2. Multiply one or both equations to get opposite coefficients. 3. Add or subtract the equations to eliminate one variable.

Tags

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 the lines of the equations plotted on a coordinate plane.

Tags

CCSS.8.EE.C.8A

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What is the significance of the slope in a system of equations?

Back

The slope indicates the steepness of the line; lines with the same slope are parallel.

Tags

CCSS.8.EE.C.8B

Front

What is the y-intercept in a linear equation?

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The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the standard form of a linear equation?

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The standard form is Ax + By = C, where A, B, and C are integers, and A should be non-negative.