Systems and Matrices

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 graph a system of equations?

Back

It means to plot the equations on a coordinate plane to find their intersection point, which represents the solution.

Front

What is a matrix?

Back

A rectangular array of numbers arranged in rows and columns.

Front

How do you determine the number of rows in a matrix?

Back

The number of rows is the first number in the matrix's dimensions (e.g., in a 7 x 3 matrix, there are 7 rows).

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

What does it mean if two lines are parallel when graphed?

Back

It means the system of equations has no solution, as the lines never intersect.

Front

What does it mean if two lines coincide when graphed?

Back

It means the system of equations has infinite solutions, as the lines overlap completely.

Front

How do you solve a system of equations using matrices?

Back

You can use methods such as the inverse matrix method or row reduction to find the values of the variables.

Front

What is the y-coordinate in a solution of a system of equations?

Back

It is the second value in the ordered pair that represents the solution (x, y).

Front

What is the purpose of using matrices in solving systems of equations?

Back

Matrices provide a structured way to organize and manipulate the coefficients and constants of the equations.