Systems of Equations: Graphing and Substitution

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved together.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for two lines to intersect in a system of equations?

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It means that there is a solution (x, y) that satisfies both equations simultaneously.

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CCSS.8.EE.C.8A

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

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By graphing both equations on the same coordinate plane and identifying the point 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?

Back

The substitution method involves solving one equation for one variable and then 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.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is a y-intercept?

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The y-intercept is the point where a line crosses the y-axis, represented as (0, b) where b is the value of y.

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How do you find the y-intercept from an equation in standard form?

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To find the y-intercept from an equation in standard form (Ax + By = C), set x = 0 and solve for y.

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CCSS.HSF-IF.C.7A

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

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.F.A.3

CCSS.8.EE.B.6

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What does the slope of a line represent in a graph?

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The slope represents the rate of change of y with respect to x, indicating how steep the line is.

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CCSS.8.EE.B.5

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What is linear regression?

Back

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation.