IM1: Solving Systems of Linear Equations by Elimination

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 equations by elimination?

Back

To manipulate the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the first step in solving the system 4x + 4y = 4 and 3x + 4y = 10 by elimination?

Back

Add the equations to eliminate y.

Front

What is the solution to the system 4x + 4y = 4 and 3x + 4y = 10?

Back

(-6, 7)

Front

What is the solution to the system 4x + 9y = 28 and -4x - y = -28?

Back

(7, 0)

Front

What does the solution of a system of linear equations represent?

Back

The point where the lines intersect, which is the ordered pair (x, y).

Front

What is an ordered pair?

Back

A pair of numbers (x, y) that represent a point in a coordinate plane.

Front

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

Back

Two or more lines on a graph that may intersect at one point, be parallel, or coincide.

Front

What does it mean if two lines are parallel in a system of equations?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide in a system of equations?

Back

The system has infinitely many solutions because the lines are the same.