Solving Systems by Graphing

Front

What is a system of equations?

Back

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

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

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.

Front

What is the solution to a system of equations?

Back

The point at which the equations intersect, representing the values of the variables that satisfy all equations in the system.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run (change in y over change in x).

Front

What does it mean if two lines intersect at a point?

Back

It means that there is a unique solution to the system of equations represented by those lines.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

How do you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating that there is no solution.

Front

What is the graphical representation of the equation y = mx + b?

Back

It represents a straight line where m is the slope and b is the y-intercept.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the lines intersect at least once.