Solving Systems using Elimination

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 directly.

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 the coefficients of one variable are opposites, allowing them to cancel out when added or subtracted.

Front

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

Back

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

Front

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

Back

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

Front

Solve using Elimination: x - y = 11 and 2x + y = 19.

Back

(10, -1)

Front

Solve using Elimination: -2x - 5y = 10 and 3x + 2y = 7.

Back

(5, -4)

Front

Solve using Elimination: -3x + 3y = -33 and 6x - 3y = 57.

Back

(8, -3)

Front

Solve using Elimination: -7x - 5y = 12 and 7x + 5y = -12.

Back

Infinitely Many Solutions

Front

Solve using Elimination: -7x + 6y = 29 and 10x + y = 16.

Back

(1, 6)

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.