Solving Systems by Elimination

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

How do you set up a system of equations from a word problem?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the problem accurately.

Front

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

Back

(-6, 7)

Front

Solve by elimination: 2x + 9y = -7 and 6x - 3y = 9.

Back

(1, -1)

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set, meaning they represent the same line in a graph.

Front

How can you check the solution of a system of equations?

Back

Substitute the solution back into both original equations to verify that both equations are satisfied.

Front

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

Back

(7, 0)

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

What is the first step in the elimination method?

Back

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

Front

Create a system of equations for: Ride charges $2 pickup + $2.50 per mile, Transport charges $2.70 per mile. How many miles until costs are equal?

Back

Let x be the number of miles. Ride: 2 + 2.5x = Transport: 2.7x.