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 set up equations for elimination?

Back

To set up equations for elimination, align the equations so that corresponding variables and constants are in the same columns, and manipulate the equations to have the same coefficient for one variable.

Front

What is the first step in solving a system of equations by elimination?

Back

The first step is to manipulate the equations (if necessary) so that the coefficients of one of the variables are the same or opposites.

Front

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

Back

(7, 0)

Front

Solve by elimination: 2x + 3y = 12 and 5x - y = 13.

Back

(3, 2)

Front

Solve by elimination: 2x + 9y = -7 and 6x - 3y = 9.

Back

(1, -1)

Front

Solve by elimination: y = 8x + 1 and y = 6x + 3.

Back

(1, 9)

Front

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

Back

(-6, 7)

Front

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

Back

A system of equations has no solution if 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

A system of equations has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.