A1 U4 System Word problems

Front

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 word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and express them in a system format.

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CCSS.HSA.CED.A.3

Front

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

Back

To solve a system of equations graphically means to plot the equations on a graph and find the point(s) where they 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.

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

How can you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, meaning they never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How do you set up an equation from a word problem involving costs?

Back

Identify the fixed costs and variable costs, then express the total cost as a function of the number of items or services.

Front

What is a linear equation?

Back

A linear equation is an equation that models a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How do you interpret the slope in a linear equation related to a word problem?

Back

The slope represents the rate of change, indicating how much one quantity changes in relation to another.

Tags

CCSS.8.EE.B.5