5.1Systems of linear equations

Front

What are systems of linear equations?

Back

A set of two or more linear equations in the same variables.

Front

What is the solution to a system of linear equations?

Back

The point where the equations intersect, satisfying all equations in the system.

Front

How can you tell if a point is a solution to a system?

Back

The (x,y) coordinates satisfy both equations.

Front

How many solutions can a system of linear equations have?

Back

One Solution, No solution, or Infinitely Many Solutions.

Front

What does it mean if a system has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations coincide, meaning they are the same line.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

Front

What is the graphical representation of a system of linear equations?

Back

The intersection points of the lines representing the equations.

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.