System of equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

It means the system has one solution, which is the point of intersection.

Front

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

Back

It means the system has no solution, as the lines never intersect.

Front

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

Back

It means the system has infinitely many solutions, as they share all points.

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 solution to the system of equations: x + 3y = 18 and -x - 4y = -25?

Back

(-3, 7)

Front

What is the solution to the system of equations: -2x + y = 10 and 4x - y = -14?

Back

(-2, 6)

Front

If a system of equations has one solution, what does that indicate about the lines?

Back

The lines intersect at exactly one point.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.

Front

What is the significance of the slope in a system of equations?

Back

The slope indicates the steepness of the line and helps determine if lines are parallel or intersecting.