Systems of Linear Equations

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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.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean if a system of linear equations has one solution?

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The lines representing the equations intersect at exactly one point.

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CCSS.8.EE.C.8A

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

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The lines representing the equations are parallel and never 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 infinitely many solutions?

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The lines representing the equations coincide, meaning they are the same line.

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CCSS.8.EE.C.8A

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How can you solve a system of linear equations graphically?

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By plotting the equations on a graph and identifying the point(s) of intersection.

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CCSS.8.EE.C.8B

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What is the substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted 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 in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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The solution is the point where the two lines intersect, which is (1, 3).

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CCSS.8.EE.C.8B

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

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CCSS.8.EE.B.6

CCSS.8.F.A.3

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How do you find the slope of a line given two points, (x1, y1) and (x2, y2)?

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CCSS.8.EE.B.5