Solve Linear Systems by Graphing Flashcard

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving 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

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.

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 they intersect at every point on that line.

Front

How do you graph a linear equation?

Back

To graph a linear equation, you can find two or more points that satisfy the equation and then draw a straight line through those points.

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.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes (positive or negative).

Front

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

Back

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

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

What is the x-intercept of a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis, found by setting y to 0 and solving for x.