Solving Linear Systems by Elimination

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

Front

What does it mean to solve a linear system by elimination?

Back

Solving a linear system by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is the elimination method?

Back

The elimination method is a technique for solving systems of equations by removing one variable, allowing for the solution of the remaining variable.

Front

How do you eliminate a variable in a linear system?

Back

To eliminate a variable, you can multiply one or both equations by a number so that when you add or subtract the equations, one variable cancels out.

Front

What is the first step in solving a system of equations by elimination?

Back

The first step is to align the equations and decide which variable to eliminate.

Front

Solve for x and y: 2x + 3y = 6 and 4x - y = 5.

Back

(2,0) - Solution found by elimination.

Front

What is a consistent system of equations?

Back

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

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the lines represented by the equations are parallel and never intersect.

Front

What is a dependent system of equations?

Back

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

Front

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

Back

Infinitely many solutions - the second equation is a multiple of the first.