6.1 Practice: Graphing Systems of Linear Equations

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What is the solution to the system of equations?

Back

The solution is the point where the two lines intersect. For example, for the equations y = 2x + 1 and y = -x + 3, the solution is (1, 3).

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How many solutions can a system of linear equations have?

Back

A system of linear equations can have one solution, no solution, or infinitely many solutions.

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CCSS.8.EE.C.8B

Front

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

Back

If two lines are parallel, it means they have no points in common, resulting in no solution for the system.

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CCSS.8.EE.C.8A

Front

What does it mean if two lines are the same in a system of equations?

Back

If two lines are the same, it means they overlap completely, resulting in infinitely many solutions.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection of the lines representing the equations.

Front

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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you determine if a system of equations has one solution?

Back

A system has one solution if the lines intersect at exactly one point.

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CCSS.8.EE.C.8A

Front

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 the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How can you tell if two lines are intersecting?

Back

Two lines are intersecting if they have different slopes and meet at a single point.

Tags

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 = 0.