Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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.

Front

How can you determine the y-intercept of a linear equation?

Back

The y-intercept is the point where the graph crosses the y-axis, which occurs when x=0.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines or curves of the equations plotted on a coordinate plane.

Front

What does it mean for a point to be a solution to a system of equations?

Back

The point's coordinates satisfy all equations in the system.

Front

How can you tell if two lines are parallel in a system of equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the slope of a line?

Back

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

Front

How do you find the slope from two points on a line?

Back

Use the formula: slope (m) = (y2 - y1) / (x2 - x1).

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What is the significance of the solution (1, -1) in a system of equations?

Back

It indicates that when x=1, y=-1 satisfies both equations in the system.

Front

What is the method of graphing used to solve systems of equations?

Back

The method involves plotting the equations on a graph and identifying the point(s) of intersection.