Systems of Equations Applications

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

How can you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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CCSS.HSA.CED.A.3

Front

What does the variable 'x' typically represent in a system of equations?

Back

In application problems, 'x' often represents the quantity of one type of item or entity being analyzed.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does the variable 'y' typically represent in a system of equations?

Back

In application problems, 'y' often represents the quantity of another type of item or entity being analyzed.

Tags

CCSS.8.EE.C.8B

Front

How do you solve a system of equations graphically?

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To solve graphically, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect, which represent the solution(s).

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method for solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

Coefficients represent the rate of change or the quantity of each variable in relation to the total, influencing the solution of the system.

Tags

CCSS.8.EE.C.8B

Front

How can you check the solution of a system of equations?

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Substitute the solution back into the original equations to verify that both equations are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a consistent system of equations?

Back

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

Tags

CCSS.8.EE.C.8A