Solving Systems by Elimination

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

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

Back

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

Front

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

Back

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

Front

How do you determine if two equations are equivalent?

Back

Two equations are equivalent if they have the same solution set, meaning they represent the same line when graphed.

Front

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

Back

(-1, -2)

Front

Solve by elimination: 7x - 9y = 29 and 7x + 2y = -15

Back

(-1, -4)

Front

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

Back

(3, 5)

Front

Solve by elimination: 4x + 4y = 4 and 3x + 4y = 10

Back

(-6, 7)

Front

What is the first step in the elimination method?

Back

The first step is to align the equations and decide which variable to eliminate.

Front

What do you do if the coefficients of the variable you want to eliminate are not the same?

Back

You can multiply one or both equations by a number to make the coefficients the same.