Solving Systems by Elimination w/ Multiplication

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations by elimination?

Back

It means to eliminate one variable by adding or subtracting the equations after possibly multiplying one or both equations by a constant.

Front

What is the elimination method?

Back

A method for solving systems of equations by removing one variable, allowing for the other variable to be solved easily.

Front

When might you need to multiply an equation in a system?

Back

To make the coefficients of one variable the same or opposites, facilitating elimination.

Front

What is the first step in solving the system 3x + 2y = 16 and 7x + y = 19 by elimination?

Back

Decide which variable to eliminate and adjust the equations accordingly.

Front

In the system 2x + 3y = 12 and 5x - y = 13, which equation should be multiplied to eliminate y?

Back

The bottom equation should be multiplied by 3.

Front

What is the result of eliminating x in the system 10x - 8y = -30 and -10x + 9y = 25?

Back

You will solve for y.

Front

What does it mean to multiply an equation by a constant?

Back

It means to multiply every term in the equation by the same number, which keeps the equation equivalent.

Front

How do you determine which variable to eliminate in a system of equations?

Back

Look for the variable that can be easily made to have the same coefficient in both equations.

Front

What is the solution to the system 3x + 2y = 16 and 7x + y = 19?

Back

(2, 5)