Systems of Equations

Front

What is a system of equations?

Back

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 infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How can you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines represented by the equations.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted 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

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

The solution is (2, 5).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into the original equations to see if both equations are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6