A.3F Algebra Systems of Equations

Front

What is a system of equations?

Back

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

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines intersect at exactly one point, which is the solution.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

How can you determine the number of solutions in a system of equations?

Back

By graphing the equations and observing their intersection points.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

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 substitution method in solving systems of equations?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable.