Systems - One, None, or Infinitely Many

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 if a linear system has one solution?

Back

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

Front

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

Back

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

Front

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

Back

It means that the equations represent the same line, and there are countless points of intersection.

Front

How can you determine if two equations represent the same line?

Back

If one equation can be transformed into the other by multiplying or dividing by a non-zero constant.

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

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

Front

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

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is the substitution method in solving systems of equations?

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 systems of equations?

Back

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