Solving Systems 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?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the elimination method?

Back

A technique for solving systems of equations by eliminating one variable, allowing for the other to be solved.

Front

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

Back

By adding or subtracting the equations after multiplying them by suitable coefficients.

Front

What is the first step in using the elimination method?

Back

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

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

Solve the system by elimination: 2x + 3y = 12 and 5x - y = 13.

Back

x = 3, y = 2

Front

Solve the system by elimination: 8x + 4y = 12 and y = -2x + 3.

Back

Infinitely many solutions

Front

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

Back

(1, -1)