Solving Systems by Elimination

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system by elimination?

Back

Solving a system by elimination 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 is the elimination method?

Back

The elimination method is a technique used to solve systems of equations by removing 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 determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

If the lines intersect at one point, there is one solution. If the lines are parallel, there is no solution. If the lines coincide, there are infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

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

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you make the coefficients of one variable the same in both equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system: 2x + 9y = -7 and 6x - 3y = 9?

Back

(1, -1)

Tags

CCSS.HSA.REI.C.9

Front

What is the solution to the system: 4x + 9y = 28 and -4x - y = -28?

Back

(7, 0)

Tags

CCSS.HSA.REI.C.9

Front

How do you write a system of equations from a word problem?

Back

Identify the variables, translate the relationships into equations, and set them equal to each other based on the problem's context.

Tags

CCSS.8.EE.C.8C

Front

What is the solution to the system: 2x + 3y = 12 and 5x - y = 13?

Back

(3, 2)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6