24-25 - Reflashcard Graphing System of Equations and Inequalities

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept and slope, then plot the y-intercept on the graph and use the slope to find another point.

Front

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

Back

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

Front

What is the meaning of 'infinite solutions' in a system of equations?

Back

It means that the equations represent the same line, so every point on the line is a solution.

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 the equations are satisfied, the point is a solution.

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables. The solution is the region where the inequalities overlap on a graph.

Front

How do you graph a system of inequalities?

Back

Graph each inequality as if it were an equation, then shade the appropriate region for each inequality. The solution is where the shaded regions overlap.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What is the y-intercept of a line?

Back

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

Front

How do you solve a system of equations graphically?

Back

Graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.