Solving Systems of Two 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 for two lines to be parallel in a system of linear equations?

Back

Parallel lines have no points in common; they do not intersect.

Front

What does it mean for two lines to intersect in a system of linear equations?

Back

Intersecting lines have exactly one point in common, which is the solution to the system.

Front

What are coincident lines in a system of linear equations?

Back

Coincident lines are lines that lie on top of each other, representing an infinite number of solutions.

Front

How do you solve a system of linear equations graphically?

Back

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

Front

What is the substitution method for solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What is the solution to the system: y = 2/3x - 2 and y = -x + 3?

Back

(3, 0)

Front

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

Back

It means the lines are parallel and do not intersect.

Front

What is the graphical representation of the solution to a system of equations?

Back

The point(s) where the lines representing the equations intersect.