systems practice w/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.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you represent a real-world problem using a system of equations?

Back

To represent a real-world problem using a system of equations, identify the variables that represent the unknowns, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

Tags

CCSS.8.EE.C.8C

Front

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

Back

Solving a system of equations graphically involves plotting the equations on a coordinate plane and finding the point(s) where the lines intersect, which represents the solution(s) to the system.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of the variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in 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 a dependent system of equations?

Back

A dependent system of equations has infinitely many solutions, as the equations represent the same line or plane in a geometric sense.

Tags

CCSS.8.EE.C.8B

Front

What is an independent system of equations?

Back

An independent system of equations has exactly one solution, where the graphs of the equations intersect at a single point.

Tags

CCSS.8.EE.C.8A

Front

What is an inconsistent system of equations?

Back

An inconsistent system of equations has no solution, as the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

How can you check if your solution to a system of equations is correct?

Back

You can check if your solution is correct by substituting the values back into the original equations to see if they satisfy all equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What role do coefficients play in a system of equations?

Back

Coefficients are the numerical factors in front of the variables in an equation. They determine the slope and position of the lines when graphed.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6