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 to the system is the set of values that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

Tags

CCSS.HSA.CED.A.3

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution in common.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for two equations to be independent?

Back

Two equations are independent if they represent different lines that intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for two equations to be dependent?

Back

Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the graphs of the equations: if they intersect at one point, there is one solution; if they are parallel, there are no solutions; if they are the same line, there are infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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 remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you check the solution of a system of equations?

Back

Substitute the values of the variables back into the original equations to verify that both equations are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where the lines intersect.

Tags

CCSS.8.EE.C.8B