Solving Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of linear equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is substitution 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 elimination 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 if a system has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system has infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

What is a unique solution in a system of equations?

Back

A single point where the lines intersect, representing one set of values for the variables.

Tags

CCSS.8.EE.C.8A

Front

How do you determine if a system of equations is consistent or inconsistent?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of a system of linear equations?

Back

The equations are represented as lines on a coordinate plane, and their intersection points represent the solutions.

Tags

CCSS.8.EE.C.8A

Front

What is the role of coefficients in a linear equation?

Back

Coefficients determine the slope and position of the line represented by the equation.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3