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, which is the point of intersection.

Front

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

Back

By plotting both equations on the same graph and identifying the point where they intersect.

Front

What is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

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

Back

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

Front

What is the graphical representation of the equation y = 3x - 2?

Back

A straight line with a slope of 3 and a y-intercept of -2.

Front

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

Back

The (x,y) coordinates must satisfy both equations.

Front

What is the y-intercept of the equation y = 4x + 2?

Back

2, which is the point where the line crosses the y-axis.

Front

What does the slope of a line represent in a graph?

Back

The rate of change of y with respect to x.

Front

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

Back

They are parallel and have no solution.