24/25 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 removing one variable, making it easier to solve for the other.

Front

How do you determine if a system of equations has infinitely many solutions?

Back

If the equations represent the same line, they have infinitely many solutions.

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

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

Back

(7,-1)

Front

Solve by elimination: 2x + 6y = -28 and x + 3y = -14.

Back

Infinitely Many Solutions

Front

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

Back

(3,5)

Front

Solve by elimination: -4x - 2y = -12 and 4x + 8y = -24.

Back

(6,-6)

Front

Solve the system of equations: 5x + y = 9 and 10x - 7y = -18.

Back

(1, 4)