Exploring Rational Expressions in Algebra I

What is the first step in solving a system of equations by substitution?

• Isolate one variable in one equation

• Substitute the isolated variable into all equations

• Graph the equations to find the intersection

• Eliminate one variable using addition or subtraction

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Why is it important to use parentheses when substituting values in equations?

• To differentiate between variables and constants

• To make the equations look clearer

• To avoid making mistakes with negative signs

• To ensure the correct order of operations is followed

Tags

CCSS.6.EE.A.2C

How can you verify that your solution to a system of equations is correct?

• Check if the solution makes the equation graphically accurate

• Substitute the solution back into only one original equation

• Solve the equations again using a different method

• Substitute the solution into both original equations to see if they hold true

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What does it mean when one kennel becomes cheaper than another after a certain number of days?

• The kennels offer the same services for different prices

• The daily rate of one kennel is always lower

• The total cost from one kennel becomes less than the other after that many days

• The processing fee of one is lower than the other

How do you set up an equation to compare the costs of two kennels over multiple days?

• Set the total costs equal to each other and solve for days

• Subtract the daily rates and solve for the number of days

• Add the processing fees and compare them directly

• Multiply the number of days by the sum of daily rate and processing fee for each kennel

What is the significance of the equation '12D + 35 < 15D + 20' in the kennel cost problem?

• It compares the processing fees of the two kennels

• It calculates the number of days after which one kennel is cheaper than the other

• It shows the daily increase in cost for one kennel over another

• It determines when the cost of one kennel exceeds the other

In the context of buying fish, what does the equation 'N + Z = 13' represent?

• The fish were bought at a discount of $13

• There are 13 fish in total, combining neon tetras and zebrafish

• Thirteen is the combined price of one neon tetra and one zebrafish

• The total cost of neon tetras and zebrafish is $13

Tags

CCSS.6.EE.B.6

What is the purpose of substituting 'N = 13 - Z' into another equation?

• To eliminate the variable Z and solve for N

• To find the value of Z by using the total number of fish

• To simplify the equation and solve for the total cost

• To isolate one variable and solve the system

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What does the solution 'N = 6, Z = 7' indicate in the context of the fish buying problem?

• The fish cost $6 and $7 each

• 6 zebrafish and 7 neon tetras were bought

• 13 fish were bought for $6 and $7 respectively

• 6 neon tetras and 7 zebrafish were bought

Tags

CCSS.8.EE.C.8C

How do you verify if the calculated number of fish is correct?

• Re-calculate using a different method

• Compare with the cost of another type of fish

• Check if substituting the numbers back into the original equations holds true

• Ask for a recount of the fish

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6