12/11/24 Exit Ticket - Systems of Equations (Elimination)

Front

What is a system of equations?

Back

A system of equations is two or more equations whose variables have the same value and show an intersection on the graph.

Front

Which variable will be eliminated in the system: 4x + 8y = 20 and -4x + 2y = -30?

Back

The variable x will be eliminated.

Front

What is the solution to the system: 4x + 8y = 20 and -4x + 2y = -30?

Back

The solution is (7,-1).

Front

What is the elimination method in 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 variable.

Front

What does it mean if two equations in a system are dependent?

Back

Dependent equations are equations that represent the same line, meaning they have infinitely many solutions.

Front

What does it mean if two equations in a system are independent?

Back

Independent equations are equations that represent different lines, meaning they have exactly one solution.

Front

What does it mean if two equations in a system are inconsistent?

Back

Inconsistent equations are equations that represent parallel lines, meaning they have no solutions.

Front

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

Back

A system has no solution if the equations represent parallel lines, which have the same slope but different y-intercepts.

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations so that like terms are in the same column.

Front

How do you eliminate a variable using the elimination method?

Back

You can eliminate a variable by adding or subtracting the equations to cancel out that variable.