Solving Systems of Equations by Elimination

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, allowing you to solve for the other variable.

Front

What is the elimination method?

Back

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

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they have no solution because they never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, and every point on that line is a solution.

Front

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

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

How can you make the coefficients of one variable the same in both equations?

Back

You can multiply one or both equations by a number to achieve the same coefficient for that variable.

Front

What is the solution to the system of equations 3x + 3y = 9 and 5x + 4y = 10?

Back

(-2, 5) is the solution.

Front

What is the solution to the system of equations x - 2y = 10 and x + 3y = 5?

Back

(8, -1) is the solution.

Front

What is the solution to the system of equations x + 3y = 5 and x = -6y + 14?

Back

(-4, 3) is the solution.