Unit 3 Flashcard 3 Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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, and any point on that line is a solution.

Front

What is the elimination method in solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation. If both equations are true, the point is a solution.

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 does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is a parallel line in the context of systems of equations?

Back

Parallel lines have the same slope but different y-intercepts, meaning they never intersect and have no solutions.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How can you graph a system of equations?

Back

By plotting each equation on the same coordinate plane and identifying points of intersection.

Front

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

Back

It means the equations represent parallel lines that never intersect.