Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of equations to have one solution?

Back

It means that the graphs of the equations intersect at exactly one point, indicating a unique solution for the variables.

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CCSS.8.EE.C.8A

Front

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

Back

It means that the graphs of the equations are parallel and never intersect, indicating that there are no values for the variables that satisfy both equations.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that the equations represent the same line, so every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How do you find the solution to a system of equations by graphing?

Back

You graph each equation on the same coordinate plane and identify the point(s) where the graphs intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

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CCSS.8.EE.B.5

Front

How do you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (difference in y-coordinates) and the run (difference in x-coordinates), and divide rise by run.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

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