Mod 6 TEST (6.1-6.4) - Systems of Equations (2024)

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

How do you solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

Front

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

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Front

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

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

Front

What is the elimination method for 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

What is the solution to the system of equations 2x + 3y = 6 and x - y = 1?

Back

The solution is (3,0).

Front

If a system of equations has infinitely many solutions, what does that indicate about the equations?

Back

It indicates that the equations are dependent, meaning they represent the same line.

Front

What is the first step in solving the system 3x + 2y = 16 and 7x + y = 19?

Back

The first step is to use either substitution or elimination to simplify the system.

Front

How can you check if your solution to a system of equations is correct?

Back

You can check by substituting the solution back into the original equations to see if both equations are satisfied.