Graphing Systems of Equations and Inequalities

Front

What is a system of equations?

Back

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

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means there is no solution to the system, as the lines never intersect.

Front

What does it mean if two lines are the same in a system of equations?

Back

It means there are infinitely many solutions, as every point on the line is a solution.

Front

How do you graph a linear equation in slope-intercept form?

Back

Identify the slope (m) and y-intercept (b) from the equation y = mx + b, then plot the y-intercept and use the slope to find another point.

Front

What is the slope of the line represented by the equation 2x + 3y = 6?

Back

The slope is -2/3 after rearranging to slope-intercept form.

Front

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

Back

Substitute the point's coordinates into both equations; if both equations are true, the point is a solution.

Front

What is the graphical representation of the solution to a system of equations with one solution?

Back

Two intersecting lines on a graph.

Front

What is the solution to the system of equations 3x + 2y = 6 and 2x - y = 1?

Back

(2, 0) after solving the system.

Front

What does the term 'feasible region' refer to in graphing inequalities?

Back

The area on a graph where all the constraints of the inequalities are satisfied.

Front

How do you find the x-intercept of a linear equation?

Back

Set y = 0 in the equation and solve for x.