Graphing Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of 2 or more equations that share the same variables.

Front

How many solutions can a system of linear equations have?

Back

0, 1, 2, or infinitely many.

Front

What does it mean if two lines intersect at a point?

Back

The system has one solution, which is the coordinates of the intersection point.

Front

What does it mean if two lines are parallel?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide?

Back

The system has infinitely many solutions because the lines are the same.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the graphical representation of a system of linear equations?

Back

It is represented by lines on a coordinate plane.

Front

What is the solution to the system of equations y = 2x + 1 and y = 2x - 3?

Back

No solution, as the lines are parallel.

Front

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

Back

(1, 3), as the lines intersect at this point.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.