Write Systems of Linear Equations

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What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How do you represent the cost of items in a system of equations?

Back

You can represent the cost of items by assigning variables to each item and creating equations based on the total cost of purchases.

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What does the variable 'x' typically represent in a cost equation?

Back

In a cost equation, 'x' often represents the cost of one type of item, such as a bottle of oil or a burger.

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CCSS.HSF.LE.B.5

Front

What does the variable 'y' typically represent in a cost equation?

Back

In a cost equation, 'y' often represents the cost of another type of item, such as an oil filter or a drink.

Tags

CCSS.8.EE.B.5

Front

How do you set up a system of equations from word problems?

Back

Identify the variables, translate the problem into equations based on the relationships described, and ensure the equations reflect the total costs or quantities.

Tags

CCSS.8.EE.C.8C

Front

What is the significance of the coefficients in a system of equations?

Back

The coefficients represent the quantity of each item being purchased in the equations.

Tags

CCSS.8.EE.C.8C

Front

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

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

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, meaning the equations do not intersect at any point.

Tags

CCSS.8.EE.C.8B

Front

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

Back

The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s) of the system.

Tags

CCSS.8.EE.C.8A

Front

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

Back

By plotting the equations on a graph and identifying the point(s) where the lines intersect.

Tags

CCSS.8.EE.C.8B