Solving Systems of Linear Equations

Front

What is a system of linear equations?

Back

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

Front

What does it mean if a system of linear equations has no solutions?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of linear equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are the same line, overlapping completely.

Front

What are the three main methods to solve systems of equations?

Back

Graphing, Substitution, Elimination.

Front

How do you solve a system of equations using the substitution method?

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 the elimination method?

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 equations?

Back

It is represented by lines on a coordinate plane.

Front

What is the solution to the system of equations y=8x+1 and y=6x+3?

Back

(1, 9)

Front

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

Back

It indicates that the system of equations has one unique solution.