Solving Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean to solve a system of linear equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the elimination method?

Back

A technique for solving systems of linear equations by adding or subtracting equations to eliminate one variable.

Front

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

Back

Multiply one or both equations by a constant to align coefficients.

Front

Solve by elimination: 4x + 9y = 28 and -4x - y = -28.

Back

(7, 0)

Front

Solve by elimination: 4x + 4y = 4 and 3x + 4y = 10.

Back

(-6, 7)

Front

What is the solution to the system: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

Front

What does it mean if two lines are parallel in the context of linear equations?

Back

They have the same slope and will never intersect, meaning no solution exists for the system.

Front

Which equation represents a parallel line to y = x + 1?

Back

y = x - 1.

Front

What is the graphical representation of a system of linear equations?

Back

The point(s) where the lines intersect represent the solution(s) to the system.