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 can you determine 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 does it mean if two lines are parallel when graphing a system of equations?

Back

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

Front

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

Back

(1, 3) - The lines intersect at this point.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, and every point on the line is a solution.

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 find the y-intercept of a linear equation?

Back

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

Front

What is the slope of a line?

Back

The slope is the ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

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

Back

It means the lines are parallel and do not intersect.