Determining Solutions in Systems of Equations

The video tutorial explains how to determine if a system of two equations is consistent or inconsistent, and whether it is dependent or independent. It covers scenarios with one solution, many solutions, and no solutions, providing methods to identify each case. The tutorial includes examples using the elimination method to illustrate these concepts.

What does it mean if a system of equations is consistent?

• It has at least one solution.

• It has no solution.

• It has exactly one solution.

• It has many solutions but is not dependent.

Tags

CCSS.8.EE.C.8B

What characterizes a dependent system of equations?

• It has no solution.

• It is inconsistent.

• It has exactly one solution.

• It has many solutions.

Tags

CCSS.8.EE.C.8B

How can you identify a system of equations with one solution?

• When the equation simplifies to a false statement.

• When you get the same value for each variable.

• When you get different values for variables.

• When you get a statement like 0=0.

Tags

CCSS.8.EE.C.8B

What indicates a system of equations has no solution?

• When it simplifies to a false statement like 2=5.

• When it simplifies to a true statement like 5=5.

• When you can find a specific value for each variable.

• When the equations are identical.

Tags

CCSS.8.EE.C.8B

In the example with equations 3x+y=17 and 4x-y=18, what is the solution?

• (5, 2)

• (2, 5)

• Many solutions

• No solution

Tags

CCSS.8.EE.C.8B

What does the solution (5, 2) indicate about the system's consistency and dependency?

• Inconsistent and independent

• Inconsistent and dependent

• Consistent and independent

• Consistent and dependent

Tags

CCSS.8.EE.C.8B

In the example with equations 2x+4y=8 and x+2y=4, what type of solution does it have?

• One solution

• No solution

• Many solutions

• Cannot be determined

Tags

CCSS.8.EE.C.8B

What does the outcome of 0=0 in a system of equations signify?

• One solution

• No solution

• Many solutions

• Inconsistency

Tags

CCSS.8.EE.C.8B

In the example with equations 3x+2y=5 and 6x+4y=8, what is the nature of its solution?

• No solution

• Many solutions

• Cannot be determined

• One solution

Tags

CCSS.8.EE.C.8B

What does a system of equations being inconsistent imply?

• It has many solutions.

• It is dependent.

• It has exactly one solution.

• It has no solution.

Tags

CCSS.8.EE.C.8B