Systems of Linear Equations (Two Variables)

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What is a system of linear equations?

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean for a solution to a system of linear equations?

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A solution must make all equations in the system true.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How is a solution to a system of linear equations represented?

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As an ordered pair (x, y).

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CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of linear equations?

Back

The intersection point(s) of the lines representing the equations.

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CCSS.8.EE.C.8B

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What does it mean if a system of linear equations has no solution?

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The lines are parallel and do not intersect.

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CCSS.8.EE.C.8A

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What does it mean if a system of linear equations has infinite solutions?

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The lines are coincident, meaning they lie on top of each other.

Tags

CCSS.8.EE.C.8A

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

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The lines intersect at exactly one point.

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CCSS.8.EE.C.8A

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What is the substitution method in solving systems of equations?

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Solving one equation for one variable and substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the elimination method in solving systems of equations?

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Adding or subtracting equations to eliminate one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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