Solving Systems by Graphing

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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. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations by graphing?

Back

Solving a system of equations by graphing involves plotting the equations on a graph and identifying the point(s) where they intersect, which represents the solution.

Front

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

Back

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Front

What does it mean if two lines on a graph are parallel?

Back

If two lines are parallel, they have the same slope and will never intersect, meaning there is no solution to the system.

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What does it mean if two lines on a graph coincide?

Back

If two lines coincide, they are the same line, which means there are infinite solutions to the system.

Front

What is the intersection point of two lines?

Back

The intersection point is the coordinate pair (x, y) where the two lines meet, representing the solution to the system of equations.

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How can you find the intersection point using a graphing calculator?

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You can input the equations into the calculator, graph them, and use the 'intersect' function to find the coordinates of the intersection point.

Front

What is the significance of the y-intercept in a linear equation?

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What is the slope of a line?

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