Algebra 2: Solving Systems of Linear Equations

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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.

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CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

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How do you solve a system of equations using graphing?

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To solve using graphing, plot each equation on the same graph and identify the point(s) where they intersect.

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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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The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

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CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

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What is the elimination method in solving systems of equations?

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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.HSA.REI.C.6

CCSS.8.EE.C.8B

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

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No solution means 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 if a system of equations has infinitely many solutions?

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Infinitely many solutions occur when the equations represent the same line, meaning 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 the number of solutions in a system of equations?

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You can determine the number of solutions by analyzing the slopes and y-intercepts of the lines represented by the equations.

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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 intersection point of two lines given by equations?

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To find the intersection point, solve the system of equations simultaneously using any method (graphing, substitution, or elimination).

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CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

Back

The graph is a straight line with a slope of 4 and a y-intercept at -1.