HA2 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 no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

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

Front

How do you represent a system of equations graphically?

Back

By plotting the equations on a coordinate plane and finding the intersection points.

Front

What is the substitution method in solving linear systems?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving linear systems?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the significance of the point (4, -1) in a linear system?

Back

It is the solution to the system, meaning it satisfies all equations in the system.

Front

How can you determine if (0,0) is a solution to a system of equations?

Back

Substitute (0,0) into each equation; if all equations are satisfied, then it is a solution.

Front

What is the general form of a linear equation in two variables?

Back

The general form is Ax + By = C, where A, B, and C are constants.

Front

What does it mean for two lines to be perpendicular in the context of linear equations?

Back

Two lines are perpendicular if the product of their slopes is -1.