Solving 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 linear system 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 linear system to have no solution?

Back

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

Front

What does it mean for a linear system to have infinitely many solutions?

Back

It means that the lines represented by the equations coincide, or are the same line.

Front

How do you solve a linear system using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

How do you solve a linear system using elimination?

Back

1. Align the equations. 2. Multiply one or both equations to get opposite coefficients. 3. Add or subtract the equations to eliminate one variable.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the point of intersection of two lines?

Back

The point where the two lines cross, representing the solution to the linear system.

Front

What is the significance of the coefficients in a linear equation?

Back

They determine the slope and position of the line on the graph.