Solving Systems by Elimination

Front

What is the elimination method in solving systems of equations?

Back

The elimination method is a technique used to solve systems of 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

What does it mean to eliminate a variable in a system of equations?

Back

To eliminate a variable means to manipulate the equations in such a way that one variable is removed, making it possible to solve for the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you determine which variable to eliminate?

Back

Choose the variable that can be easily eliminated by adding or subtracting the equations, often based on the coefficients of the variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in the elimination method?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve by elimination: 2x + 3y = 6 and 4x + 6y = 12. What is the solution?

Back

There are infinitely many solutions, as the second equation is a multiple of the first.

Tags

CCSS.8.EE.C.8B

Front

Solve by elimination: 3x + 2y = 12 and 6x + 4y = 24. What is the solution?

Back

There are infinitely many solutions, as the second equation is a multiple of the first.

Tags

CCSS.8.EE.C.8B

Front

Solve by elimination: 5x - 3y = 7 and 10x - 6y = 14. What is the solution?

Back

There are infinitely many solutions, as the second equation is a multiple of the first.

Tags

CCSS.8.EE.C.8B

Front

Solve by elimination: 4x + 5y = 20 and 2x + 3y = 12. What is the solution?

Back

(2, 2)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.

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 never intersect.

Tags

CCSS.8.EE.C.8A