Solve 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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

A system has infinite solutions when the equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

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

Back

A system has no solution when the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

How do you determine if two equations are equivalent?

Back

Two equations are equivalent if they can be transformed into one another through algebraic manipulation, such as multiplying or dividing by a non-zero constant.

Tags

CCSS.8.EE.C.7A

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 variable are opposites.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you manipulate equations to prepare for elimination?

Back

You can multiply one or both equations by a constant to make the coefficients of one variable opposites.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system: 4x + 4y = 10 and 4x + 4y = 10?

Back

The solution is infinite solutions, as both equations are identical.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system: 3x + 7y = 16 and 3x + 7y = 32?

Back

The solution is no solution, as the equations represent parallel lines.

Tags

CCSS.8.EE.C.8B

Front

How do you solve the system: x + 6y = 17 and x - 3y = 8 using elimination?

Back

First, manipulate the equations to eliminate x or y, then solve for the remaining variable and substitute back to find the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system: 7x - y = -10 and -7x + 5y = -6?

Back

The solution is (-2, -4).

Tags

CCSS.HSA.REI.C.9