Systems of Linear Equations - Graphing

Front

What is a system of linear equations?

Back

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

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

Back

It means that the lines representing the equations are parallel and never intersect.

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

Back

It means that the lines representing the equations intersect at exactly one point.

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

Back

It means that the lines representing the equations are the same line, overlapping completely.

Front

How do you graph a linear equation?

Back

You can graph a linear equation by finding two or more points that satisfy the equation and connecting them with a straight line.

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).

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What is the y-intercept of a line?

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

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

Back

The solution is the point where the graphs of the equations intersect.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method for solving systems of equations?

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