Solving Systems of Linear Equations

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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 the graphical representation of a system of linear equations?

Back

The intersection points of the lines representing the equations.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two lines are parallel in a system of linear equations?

Back

The system has no solution because the lines never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two lines coincide in a system of linear equations?

Back

The system has infinite solutions because the lines are the same.

Tags

CCSS.8.EE.C.8A

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate a variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that value into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you determine the solution of a system of equations graphically?

Back

By finding the point(s) where the lines intersect.

Tags

CCSS.8.EE.C.8B

Front

What is a unique solution in a system of linear equations?

Back

A single point where the lines intersect, indicating one solution for the variables.

Tags

CCSS.8.EE.C.8A

Front

What is the significance of the coefficients in a linear equation?

Back

They determine the slope and position of the line on a graph.