6.5 - Applying 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 the substitution method in solving linear 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 linear equations?

Back

A method that involves adding or subtracting equations 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 is the graphical method for solving linear equations?

Back

Plotting the equations on a graph and finding the point(s) where they intersect.

Tags

CCSS.8.EE.C.8B

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 infinitely many solutions because the lines are the same.

Tags

CCSS.8.EE.C.8A

Front

What is the first step in using the elimination method?

Back

Align the equations so that corresponding variables and constants are in the same columns.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you determine the best method to solve a system of linear equations?

Back

Consider the complexity of the equations and the number of variables; choose substitution for simpler equations and elimination for more complex ones.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system: 2x + 3y = 6 and x - y = 1?

Back

x = 3, y = 0.

Tags

CCSS.HSA.REI.C.9