Solving 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, and any point on that line is a solution to the system.

Front

Solve by elimination: 4x + 12y = -1 and -3x - 9y = 0. What is the solution?

Back

No solution.

Front

Solve by elimination: 2x + 9y = -7 and 6x - 3y = 9. What is the solution?

Back

(1, -1).

Front

Solve by elimination: 4x + 8y = 20 and -4x + 2y = -30. What is the solution?

Back

(7, -1).

Front

Solve by elimination: -9x - 4y = -20 and 5x + 4y = 4. What is the solution?

Back

(4, -4).

Front

Solve for x: x - y = -19 and 5x + y = 1. What is the value of x?

Back

x = -3.

Front

What is the first step in the elimination method?

Back

The first step is to align the equations so that corresponding variables and constants are in the same columns.

Front

What do you do if the coefficients of one variable are not the same in both equations?

Back

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