System of Equations Practice 12/4

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 a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, represented as (x,y).

Front

How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

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 equations?

Back

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

Front

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

Back

It means that there is a unique solution to the system of equations.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve.

Front

What is the significance of the point (1,3) in a system of equations?

Back

It is the solution to the system, indicating where the two lines intersect.

Front

What does it mean if the solution to a system of equations is (4,-2)?

Back

It means that the two equations intersect at the point (4,-2) on the graph.