Solving Systems of Equations 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 to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

What is a y-intercept?

Back

The point where a line crosses the y-axis, represented as (0, y).

Front

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

Back

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

Front

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

Back

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

Front

What does it mean if two lines coincide when graphing a system of equations?

Back

It means there are infinite solutions, as the lines are the same.

Front

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

Back

By identifying the intersection point(s) of the graphs of the equations.

Front

What is the significance of the intersection point in a system of equations?

Back

It represents the values of the variables that satisfy all equations in the system.

Front

What is the slope of a line?

Back

The rate of change of y with respect to x, often represented as 'm' in the equation y = mx + b.