Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the graphical representation of a system of equations?

Back

The point(s) where the graphs of the equations intersect.

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

How do you represent a system of equations in matrix form?

Back

Using an augmented matrix that includes the coefficients of the variables and the constants from the equations.

Front

What is the solution to the system of equations 4x + 9y = 28 and -4x - y = -28?

Back

(7, 0)

Front

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

Back

If the equations represent parallel lines, they will never intersect.

Front

What is the meaning of a consistent system of equations?

Back

A system that has at least one solution.

Front

What is the meaning of an inconsistent system of equations?

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A system that has no solutions.