Solving Systems by Elimination Method

Front

What is the elimination method in solving systems of equations?

Back

The elimination method is a technique used to solve systems of equations by eliminating one variable, allowing the other variable to be solved easily.

Front

How do you eliminate a variable in a system of equations?

Back

To eliminate a variable, you can multiply one or both equations by a number so that when you add or subtract the equations, one variable cancels out.

Front

Solve by elimination: 7x + y = -9 and -3x - y = 5

Back

(-1, -2)

Front

Solve by elimination: 9x - 4y = 7 and x - 4y = -17

Back

(3, 5)

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines that never intersect.

Front

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

Back

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

Solve the system by multiplication: 3x + 2y = 16 and 7x + y = 19

Back

(2, 5)

Front

Solve by elimination: x - y = 11 and 2x + y = 19

Back

(10, -1)

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 solving a system of equations by elimination?

Back

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