8.1 & 8.2 Solving Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

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

Back

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

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines representing the equations.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

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

Back

A system has no solution if the lines are parallel, meaning they never intersect.

Front

Back

The solution is (3, 1).

Front

What does it mean if two equations are dependent?

Back

Dependent equations are those that represent the same line, resulting in infinite solutions.

Front

What is the difference between consistent and inconsistent systems of equations?

Back

Consistent systems have at least one solution, while inconsistent systems have no solutions.

Front

Back

The solution is (4, -2).