Linear Systems Review

Front

What is a linear system?

Back

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

Front

What does it mean if two lines intersect at a point?

Back

It means the system has one unique solution, which is the point of intersection.

Front

What does it mean if two lines are parallel?

Back

It means the system has no solutions, as the lines never intersect.

Front

What does it mean if two lines are the same?

Back

It means the system has infinite solutions, as every point on the line is a solution.

Front

What is the substitution method?

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?

Back

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

Front

Solve the system using substitution: y - 2x = 3, x - y = 3.

Back

(-6, -9)

Front

Solve the system using elimination: y + x = 3, -y + 2x = 9.

Back

(4, -1)

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

How can you determine if a system has no solutions graphically?

Back

If the lines are parallel and never intersect.