Solve Systems Of Equations By Inspection

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What is a system of equations?

Back

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

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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 infinitely many solutions?

Back

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

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CCSS.8.EE.C.8A

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

Back

It means that the equations represent parallel lines that never intersect.

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CCSS.8.EE.C.8A

Front

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

Back

It means that the equations represent two lines that intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

How can you determine if two equations have the same slope?

Back

If the coefficients of x in both equations are equal, the slopes are the same.

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CCSS.8.EE.C.8B

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

Back

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.F.A.3

CCSS.8.EE.B.6

Front

If two equations are identical, what can be said about their solutions?

Back

They have infinitely many solutions.

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CCSS.8.EE.C.8B

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.

Tags

CCSS.8.EE.C.8A

Front

How do you solve a system of equations by inspection?

Back

By visually identifying the point of intersection of the lines represented by the equations.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, indicating the value of y when x = 0.