Solving Systems - 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 where the lines cross.

Front

How can you find the solution to a system of equations using 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) - The lines intersect at this point.

Front

What does it mean if two lines are parallel on a graph?

Back

They have no solution because they never intersect.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

What is the slope of a line?

Back

The rate at which the line rises or falls, calculated as the change in y over the change in x.

Front

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

Back

Substitute the point's coordinates into both equations; if both equations are true, the point 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

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

Back

The lines representing the equations are parallel and do not intersect.