Solving Systems of Equations by Graphing

Front

The solution to a system of equations is the place at which the lines ___________.

Back

intersect.

Front

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

Back

They are parallel and will never intersect, meaning there is no solution.

Front

What is the graphical representation of a system of equations?

Back

It is the intersection point(s) of the lines representing the equations.

Front

What does it indicate if two lines coincide on a graph?

Back

The system has infinite solutions.

Front

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

Back

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

Front

What is the first step in solving a system of equations by graphing?

Back

Graph each equation on the same coordinate plane.

Front

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

Back

The lines are parallel and do not intersect.

Front

If the equations of two lines are y = 2x + 3 and y = 2x - 1, what can be said about their solutions?

Back

They have no solution because the lines are parallel.

Front

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

Back

(1, 3) - the point where the two lines intersect.

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.