Linear Systems

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Front

What does it mean for a system of equations to have one solution?

Back

It means that the lines represented by the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solutions?

Back

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

Front

What does it mean for a system of equations to have many solutions?

Back

It means that the lines represented by the equations are the same line, so they intersect at infinitely many points.

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

Front

What is the solution to the system of equations y = 4x + 1 and 3x + 2y = 13?

Back

(1, 5)

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 slope is a measure of how steep a line is, calculated as the rise over run.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis.

Front

How do you find the solution of a linear system graphically?

Back

By plotting the equations on a graph and identifying the point of intersection.