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

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, meaning they have the same slope but different y-intercepts.

Front

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

Back

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

Front

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

Back

(-1, -2)

Front

Solve by elimination: 4x + 9y = 28 and -4x - y = -28

Back

(7, 0)

Front

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

Back

(-1, 1)

Front

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

Back

(3, 5)

Front

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

Back

(-1, -4)

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

How can you make the coefficients of one variable the same in both equations?

Back

You can multiply one or both equations by a number to achieve the same coefficient for the variable you want to eliminate.