Substitution and Elimination

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is elimination in solving systems of equations?

Back

Elimination is a method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other variable.

Front

Solve for x and y: 2x − 3y = −1, y = x − 1

Back

(4, 3)

Front

What is the solution to the system of equations: 3x + 2y = 16, 14x + 2y = 38?

Back

(2, 5)

Front

Solve the system: x + y = 19, y = 3x - 1

Back

(5, 14)

Front

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

Back

A consistent system has at least one solution.

Front

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

Back

An inconsistent system has no solutions.

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, as the equations represent the same line.

Front

Solve for x and y: 4x + 8y = 20, -4x + 2y = -30

Back

(7, -1)

Front

What is the first step in the substitution method?

Back

Solve one of the equations for one variable in terms of the other variable.