Systems of Equations: Substitution/Graphing

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations in the system simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What are the two main methods for solving systems of equations?

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The two main methods for solving systems of equations are substitution and graphing.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How does the substitution method work?

Back

In the substitution method, one equation is solved for one variable, and then that expression is substituted into the other equation to find the values of the variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean for two lines to intersect in the context of systems of equations?

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If two lines intersect, it means there is a unique solution to the system of equations, represented by the point of intersection.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations?

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The graphical representation of a system of equations consists of the graphs of the equations plotted on the same coordinate plane.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of parallel lines in a system of equations?

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Parallel lines indicate that there is no solution to the system of equations, as the lines never intersect.

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CCSS.8.EE.C.8A

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What does it mean if two lines are coincident?

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If two lines are coincident, it means they lie on top of each other, representing infinitely many solutions to the system of equations.

Tags

CCSS.8.EE.C.8A

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How can you determine the solution of a system of equations graphically?

Back

The solution of a system of equations can be determined graphically by finding the point(s) where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the first step in solving a system of equations using substitution?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the standard form of a linear equation?

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The standard form of a linear equation is Ax + By = C, where A, B, and C are constants.