Graphing Systems of Equations

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

They have no solutions because they never intersect.

Front

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

Back

They have infinitely many solutions because every point on the line is a solution.

Front

What does it mean if two lines intersect at one point in a system of equations?

Back

They have one solution, which is the point of intersection.

Front

How do you graph a linear equation?

Back

You can plot points that satisfy the equation and connect them with a straight line.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of the equation y = 2x + 3?

Back

The y-intercept is 3, which is the point (0, 3) on the graph.

Front

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

Back

By finding the point where the two lines intersect.

Front

What does it mean if a system of equations has no solution?

Back

The lines are parallel and do not intersect.

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

(1, 3) is the solution.