Solutions to linear system from graphs

Front

What is a linear system of equations?

Back

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

Front

What does it mean when a linear system has no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

How can you determine the solution to a system of equations from a graph?

Back

By identifying the point(s) where the lines intersect on the graph.

Front

What does it mean when a linear system has infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the slope of a line?

Back

The measure of the steepness of the line, calculated as the rise over run.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

How do you find the x-intercept of a line?

Back

By setting y to 0 in the equation and solving for x.

Front

What is the significance of the point (0,0) in a linear system?

Back

It is the origin and can be a solution if it satisfies the equations.