Alg.2

Front

What is a system of equations?

Back

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 to solve a system of equations?

Back

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

Front

What is a determinant in a matrix?

Back

A scalar value that is a function of the entries of a square matrix, providing important properties such as whether the matrix is invertible.

Front

How do you evaluate the determinant of a 2x2 matrix?

Back

Front

What is the graphical interpretation of a system of linear equations?

Back

Each equation represents a line in a coordinate plane, and the solution is the point(s) where the lines 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

What is the significance of a zero determinant?

Back

A zero determinant indicates that the matrix is singular, meaning it does not have an inverse and the system of equations may have no solutions or infinitely many solutions.

Front

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

Back

If the lines represented by the equations are parallel, they will never intersect, indicating no solution.

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 that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.