Solutions for Systems of Equations

Front

What does the graph of a system of equations with no solution look like?

Back

Parallel lines.

Front

How many solutions does a system of equations with no solution have?

Back

No solution.

Front

How many solutions do intersecting lines have?

Back

One solution.

Front

Given the equations y=2x+3 and y=-4x+3, how many solutions does this system have?

Back

One solution.

Front

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

Back

Intersecting lines.

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 are parallel in a system of equations?

Back

They have no points in common, hence no solution.

Front

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

Back

The same line represented by both equations.

Front

What is the solution of a system of equations represented by intersecting lines?

Back

The point where the lines intersect.

Front

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

Back

It determines the steepness and direction of the line.