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?

Back

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

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CCSS.8.EE.C.8A

Front

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

Back

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

Front

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is a y-intercept?

Back

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?

Back

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?

Back

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.EE.B.6

CCSS.8.F.A.3

Front

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

Front

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.