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 for two lines to intersect on a graph?

Back

It means that the two equations have a common solution, represented by the point of intersection.

Front

How do you find the y-intercept of a line?

Back

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

Front

What is the slope of a line?

Back

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

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases.

Front

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

Back

The point where the graphs of the equations intersect.

Front

What does it mean if two lines are parallel?

Back

It means they have the same slope and will never intersect, indicating no solution to the system.

Front

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

Back

It is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

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

Back

Substitute the point's coordinates into each equation; if both equations are satisfied, it is a solution.

Front

What is the meaning of 'ALL OF THE ABOVE' in the context of solutions to systems of equations?

Back

It indicates that the solution can be a single point, infinitely many points, or no points at all.