Systems of Equations - 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 is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What are the methods for solving systems of equations?

Back

1. Graphing 2. Substitution 3. Elimination 4. Matrix methods

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does the elimination method involve?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method?

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

How do 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 represent the same scenario.

Tags

CCSS.HSA.CED.A.3

Front

What is the first step in solving a system of equations word problem?

Back

Identify the variables and write down the equations based on the information given in the problem.

Tags

CCSS.8.EE.C.8C

Front

If Joe bought 10 cups of coffee and 5 doughnuts for $16.50, how can we express this as an equation?

Back

10c + 5d = 16.50, where c is the cost of coffee and d is the cost of doughnuts.

Tags

CCSS.HSA.CED.A.3

Front

In the problem about Amy and Adam selling cookies, how can we express their sales as equations?

Back

10s + 2o = 56 (Amy's sales) 9s + 3o = 60 (Adam's sales), where s is the price of sugar cookies and o is the price of oatmeal cookies.

Tags

CCSS.8.EE.C.8C

Front

What does it mean if two equations in a system have the same slope?

Back

If two equations have the same slope, they are parallel and do not intersect, meaning there is no solution to the system.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the intersection point of two equations?

Back

The intersection point represents the solution to the system of equations, indicating the values of the variables that satisfy both equations.

Tags

CCSS.8.EE.C.8B