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 infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

How can you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points 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 does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions.

Front

What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

The solution is (2, 5).

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into the original equations to see if both equations are satisfied.