Elimination method

Front

What is the Elimination Method in solving systems of equations?

Back

The Elimination Method is a technique used to solve systems of linear equations by eliminating one variable, allowing for the other variable to be solved directly.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you eliminate a variable in the Elimination Method?

Back

To eliminate a variable, you can add or subtract the equations in such a way that one variable cancels out.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in using the Elimination Method?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve using the Elimination Method: 2x + 3y = 6 and 4x + 6y = 12.

Back

No solution (the second equation is a multiple of the first, indicating they represent the same line).

Tags

CCSS.8.EE.C.8B

Front

Solve using the Elimination Method: x + y = 10 and x - y = 2.

Back

(6, 4) - x = 6, y = 4.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

It means that the lines represented by the equations are parallel and will never intersect.

Tags

CCSS.8.EE.C.8A

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 thus every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

Solve using the Elimination Method: 3x + 2y = 12 and 6x + 4y = 24.

Back

No solution (the second equation is a multiple of the first).

Tags

CCSS.8.EE.C.8B

Front

Solve using the Elimination Method: 5x - 2y = 3 and 3x + 2y = 15.

Back

(3, 0).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the coefficients in the Elimination Method?

Back

The coefficients determine how the equations can be manipulated to eliminate a variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6