Pre-Unit 3 Assessment

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 for a system of equations to be independent?

Back

A system is independent if it has exactly one solution, meaning the lines intersect at one point.

Front

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

Back

A system is dependent if it has infinitely many solutions, meaning the equations represent the same line.

Front

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

Back

A system is inconsistent if it has no solutions, meaning the lines are parallel and never intersect.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

How do you solve a system of equations using elimination?

Back

1. Align the equations. 2. Multiply if necessary to get coefficients to match. 3. Add or subtract the equations to eliminate one variable.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection points represent the solutions.

Front

What is the solution to the system of equations x + 2y = 4 and 3x + 6y = 12?

Back

The solution is dependent; the equations represent the same line.

Front

What is the solution to the system of equations using substitution: x + y = 3 and y = 2?

Back

The solution is x = 1, y = 2.

Front

What is the solution to the system of equations using elimination: 2x + 3y = 6 and 4x + 6y = 12?

Back

The solution is dependent; the equations represent the same line.