Solving Systems by Elimination

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system by elimination?

Back

Solving a system by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is the elimination method?

Back

The elimination method is a technique used to solve systems of equations by eliminating one variable, allowing for 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 when added or subtracted, one variable cancels out.

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.

Front

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

Back

If a system has no solution, 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

If a system has infinitely many solutions, it means the equations represent the same line, and every point on that line is a solution.

Front

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

Back

(7, -1)

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Solve by elimination: x + 9y = 8 and -6x - 9y = -3.

Back

(-1, 1)

Front

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

Back

(-1, -2)