Systems of Equations

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

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

A system has one solution when the graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

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

Back

A system has no solution when the graphs of the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

A system has infinitely many solutions when the equations represent the same line, meaning they intersect at every point on that line.

Tags

CCSS.8.EE.C.8B

Front

How do you represent a linear equation in slope-intercept form?

Back

A linear equation in slope-intercept form is represented as 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

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What is the slope of the line represented by the equation y = 2x + 3?

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The slope of the line is 2.

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CCSS.8.EE.B.5

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What is the y-intercept of the line represented by the equation y = -4x + 5?

Back

The y-intercept of the line is 5.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you determine if a system of equations is consistent or inconsistent?

Back

A system is consistent if it has at least one solution; it is inconsistent if it has no solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of the solution to a system of equations?

Back

The solution is represented by the point(s) where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

If two lines intersect at a point, what can you say about their slopes?

Back

If two lines intersect at a point, their slopes are different.

Tags

CCSS.8.EE.B.5