Solving Systems by Elimination Review

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

When is it best to use the elimination method?

Back

The elimination method is best used when the coefficients of one variable are the same or can be easily manipulated to be the same.

Front

Solve by elimination: 2x + 3y = 6 and 4x + 6y = 12.

Back

(0, 2) - This system has infinitely many solutions.

Front

What does it mean if two equations are dependent?

Back

Dependent equations are those that represent the same line, resulting in infinitely many solutions.

Front

What does it mean if two equations are inconsistent?

Back

Inconsistent equations are those that represent parallel lines, resulting in no solution.

Front

Solve using elimination: 3x + 2y = 12 and 6x + 4y = 24.

Back

(0, 6) - This system has infinitely many solutions.

Front

What is substitution in solving systems of equations?

Back

Substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

Solve using substitution: y = 2x + 1 and x + y = 5.

Back

(2, 5) - The solution is found by substituting y in the second equation.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.

Front

Solve by elimination: 5x - 2y = 3 and 10x - 4y = 6.

Back

(0, -3) - This system has infinitely many solutions.