Solving Linear Systems

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What is a linear system?

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A linear system is a collection of one or more linear equations involving 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 for a system of equations to have one solution?

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It means that the lines represented by the equations intersect at exactly one point.

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CCSS.8.EE.C.8A

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

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It means that the lines represented by the equations are parallel and 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 that the lines represented by the equations coincide, or are the same line.

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CCSS.8.EE.C.8A

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How do you represent a system of equations graphically?

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By plotting the lines of each equation on the same coordinate plane.

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CCSS.8.EE.C.8B

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What is the substitution method in solving linear systems?

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The substitution method involves solving one equation for one variable and substituting 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 in solving linear systems?

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The elimination method involves adding or subtracting equations 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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What is the point of intersection in a linear system?

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The point of intersection is the solution to the system, representing the values of the variables that satisfy all equations.

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CCSS.8.EE.C.8B

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How can you check if a solution is correct for a system of equations?

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By substituting the solution back into the original equations to see if they hold true.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the standard form of a linear equation?

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The standard form is Ax + By = C, where A, B, and C are integers, and A is non-negative.