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 infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

By analyzing the slopes and intercepts of the lines represented by the equations.

Front

What is the substitution method in 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 in 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 graphical method for solving systems of equations?

Back

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

Front

What is the solution to the system of equations 2x + 3y = 6 and 4x + 6y = 12?

Back

Infinitely Many Solutions.

Front

Solve the system using elimination: 3x + 2y = 12 and 6x + 4y = 24.

Back

Infinitely Many Solutions.

Front

Solve the system using substitution: y = 2x + 3 and x + y = 7.

Back

(2, 3).