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 that are solved together.

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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 a unique solution?

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It means there is exactly one set of values for the variables that satisfies all equations in the system.

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CCSS.8.EE.C.8B

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

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It means the equations represent parallel lines that never intersect.

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CCSS.8.EE.C.8A

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

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It means the equations represent the same line, so every point on the line is a solution.

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CCSS.8.EE.C.8A

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How can you determine if two lines are parallel?

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If they have the same slope but different y-intercepts.

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CCSS.8.EE.B.6

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What is the slope-intercept form of a linear equation?

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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

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How do you find the solution to a system of equations graphically?

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By plotting the equations on a graph and identifying the point(s) where they intersect.

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CCSS.8.EE.C.8B

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What is the substitution method for solving systems of equations?

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A method where you solve one equation for one variable and substitute that expression into the other equation.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the elimination method for solving systems of equations?

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A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean for two lines to be skew?

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They are non-parallel lines that do not intersect and exist in different planes.

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CCSS.HSG.CO.A.1