Solve Systems of Equations by Elimination (+/-)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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 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

What do you do if the coefficients of one variable are the same in both equations?

Back

You can subtract one equation from the other to eliminate that variable.

Front

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

Back

It means 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

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

Front

Solve by elimination: 3x + 7y = 23 and -3x - 7y = -17.

Back

No solution.

Front

Solve by elimination: 4x + 8y = 20 and -4x + 2y = -30.

Back

(7, -1).

Front

Solve by elimination: -4x - 6y = 6 and 4x + 6y = -4.

Back

No solution.

Front

Solve by elimination: -6x + 5y = 1 and 6x + 4y = -10.

Back

(-1, -1).