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 to the system is the point(s) where the equations intersect.

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

Back

A system of equations has one solution when the graphs of the equations intersect at exactly one point.

Front

How can you determine the solution of a system of equations by graphing?

Back

To determine the solution by graphing, plot the equations on a coordinate plane and identify the point where the lines intersect.

Front

What is the graphical representation of a system of equations with no solution?

Back

The graphical representation of a system with no solution consists of two parallel lines that never intersect.

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What is the graphical representation of a system of equations with infinitely many solutions?

Back

The graphical representation of a system with infinitely many solutions consists of two lines that overlap completely.

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How do you find the coordinates of the intersection point of two lines?

Back

To find the coordinates of the intersection point, solve the equations simultaneously or graph the lines and identify the point where they meet.

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What is the significance of the point (-3, -8) in a system of equations?

Back

The point (-3, -8) is the solution to a specific system of equations, meaning it satisfies both equations in the system.

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What does the point (1, -4) represent in the context of a system of equations?

Back

The point (1, -4) is the solution to a system of equations, indicating the values of the variables that make both equations true.

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What is the first step in solving a system of equations by graphing?

Back

The first step is to rearrange each equation into slope-intercept form (y = mx + b) if necessary, to easily identify the slope and y-intercept.

Front

What is slope-intercept form?

Back

Slope-intercept form is a way of writing linear equations as y = mx + b, where m is the slope and b is the y-intercept.