Solving Systems by Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved simultaneously.

Front

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

Back

A point is a solution if its (x,y) coordinates satisfy all equations in the system.

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, and every point on that line is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines or curves of the equations plotted on a coordinate plane.

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 connect them with a straight line.

Front

What is the significance of the intersection point of two lines in a graph?

Back

The intersection point represents the solution to the system of equations, where both equations are satisfied.

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

How can you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point where the lines intersect.