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.

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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.EE.B.6

CCSS.8.F.A.3

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.

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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.