Solving Systems

Front

What is the solution to the system of equations represented by the point (1, -1)?

Back

The solution is the point where the two lines intersect, which is (1, -1).

Front

If a system of equations has no solution, what does the graph look like?

Back

The graph consists of parallel lines that never intersect.

Front

What does it mean if a system of equations has 0 solutions?

Back

It means that the lines represented by the equations are parallel and do not intersect.

Front

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

Back

It indicates that the lines intersect at exactly one point.

Front

Solve the system by elimination: -4x - 4y = 0 and 4x + 4y = 0.

Back

The system has an infinite number of solutions.

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 be intersecting?

Back

It means they cross at one point, which represents the solution to the system.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

The lines overlap completely, representing the same line.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.