Solving Linear Systems by Graphing

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving 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 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 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 infinitely many solutions?

Back

It means that the lines represented by the equations coincide, or are the same line.

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CCSS.8.EE.C.8A

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into each equation. If both equations are satisfied, the point is a solution.

Front

Back

It is a straight line 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

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run between two points on the line.

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CCSS.8.EE.B.5

Front

How can you find the solution to a system of equations by graphing?

Back

Graph both equations on the same coordinate plane and identify the point(s) where the lines intersect.

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CCSS.8.EE.C.8B

Front

What does the term 'intersect' mean in the context of linear equations?

Back

To intersect means that the lines cross at a point, which represents the solution to the system.

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CCSS.8.EE.C.8A

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is zero.