Systems of Equations

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What is a system of equations?

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

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It means the system has no solutions because the lines never intersect.

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CCSS.8.EE.C.8A

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How can you determine the number of solutions in a system of equations?

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By analyzing the slopes and y-intercepts of the equations.

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CCSS.8.EE.C.8B

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What is the solution of a system of equations?

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The point where the graphs of the equations intersect.

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CCSS.8.EE.C.8B

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What does it mean if two equations represent the same line?

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The system has infinitely many solutions.

Tags

CCSS.8.EE.C.8B

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

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The slope is 3.

Tags

CCSS.8.EE.B.5

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If a system of equations has one solution, what does that indicate about the lines?

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The lines intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

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

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The point of intersection of the lines on a graph.

Tags

CCSS.8.EE.C.8A

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What happens to the solutions if the slopes of two lines are equal but the y-intercepts are different?

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The system has no solutions.

Tags

CCSS.8.EE.C.8B

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How can you express a system of equations in standard form?

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By writing the equations in the form Ax + By = C.