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Questions and Answers
Katrina has $2.50 in nickels and dimes, totaling 36 coins. Which system of equations correctly models this situation, where n is the number of nickels and d is the number of dimes?
Katrina has $2.50 in nickels and dimes, totaling 36 coins. Which system of equations correctly models this situation, where n is the number of nickels and d is the number of dimes?
- $n + d = 2.50, 0.05n + 0.10d = 36$
- $0.10n + 0.05d = 2.50, n + d = 36$
- $0.05n + 0.10d = 2.50, n + d = 36$ (correct)
- $n + d = 36, n + d = 2.50$
Kory drives from Edmonton to Lloydminster and back. The drive to Lloydminster averages 96 km/h, and the return trip averages 100 km/h. The total driving time is 5.1 hours. Which equation represents the relationship between the time to Lloydminster (t1) and the time back to Edmonton (t2)?
Kory drives from Edmonton to Lloydminster and back. The drive to Lloydminster averages 96 km/h, and the return trip averages 100 km/h. The total driving time is 5.1 hours. Which equation represents the relationship between the time to Lloydminster (t1) and the time back to Edmonton (t2)?
- $t_1 - t_2 = 5.1$
- $96t_1 = 100t_2$
- $t_1 + t_2 = 5.1$ (correct)
- $96t_1 + 100t_2 = 5.1$
James invests a total of $5000 in two different investments. One earns 2.9% interest, and the other earns 4.5% interest. The total interest earned is $196.20. If x represents the amount invested at 2.9% and y represents the amount invested at 4.5%, which system of equations models this?
James invests a total of $5000 in two different investments. One earns 2.9% interest, and the other earns 4.5% interest. The total interest earned is $196.20. If x represents the amount invested at 2.9% and y represents the amount invested at 4.5%, which system of equations models this?
- $0.029x + 0.045y = 196.20, x = y$
- $0.029x + 0.045y = 5000, x + y = 196.20$
- $x + y = 5000, 0.029x + 0.045y = 196.20$ (correct)
- $x + y = 196.20, 0.029x + 0.045y = 5000$
Given the system of equations $x + 2y = 0$ and $x + 5y = b$, which has a solution $(-2, a)$, what is the value of a?
Given the system of equations $x + 2y = 0$ and $x + 5y = b$, which has a solution $(-2, a)$, what is the value of a?
Given the system of equations $x + 2y = 0$ and $x + 5y = b$ with the solution $(-2, a)$, determine the value of b.
Given the system of equations $x + 2y = 0$ and $x + 5y = b$ with the solution $(-2, a)$, determine the value of b.
Solve the following system of equations using substitution: $x = 2y - 2$ and $3x - y = 4$. What is the value of y?
Solve the following system of equations using substitution: $x = 2y - 2$ and $3x - y = 4$. What is the value of y?
James invests $x at 2.9% and $y at 4.5%. If he invests $1000 more in the 4.5% investment than the 2.9% investment, which equation accurately represents this relationship?
James invests $x at 2.9% and $y at 4.5%. If he invests $1000 more in the 4.5% investment than the 2.9% investment, which equation accurately represents this relationship?
Kory drives from Edmonton to Lloydminster and back. Going to Lloydminster, he drives with an average speed of 96 km/h. For the return trip, he averages a speed of 100 km/h. If the distance between the two cities is d, Which equation can be used to represent that the distance is the same in each direction?
Kory drives from Edmonton to Lloydminster and back. Going to Lloydminster, he drives with an average speed of 96 km/h. For the return trip, he averages a speed of 100 km/h. If the distance between the two cities is d, Which equation can be used to represent that the distance is the same in each direction?
Katrina has n nickels and d dimes, totaling 36 coins. If she had twice as many nickels and half as many dimes, she would have 42 coins. Which system of equations could be used to determine the original number of nickels and dimes?
Katrina has n nickels and d dimes, totaling 36 coins. If she had twice as many nickels and half as many dimes, she would have 42 coins. Which system of equations could be used to determine the original number of nickels and dimes?
Flashcards
Substitution Method
Substitution Method
A method to solve systems of equations by solving one equation for one variable and substituting that expression into the other equation.
System of Equations
System of Equations
A set of two or more equations containing the same variables.
Solution to a System
Solution to a System
The point (x, y) that satisfies both equations in a system.
Solve a System of Equations
Solve a System of Equations
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Study Notes
Systems of Equations - Substitution Method
- Explores problems involving systems of equations, solvable through the substitution method.
Example 3
- Katrina has $2.50 in nickels and dimes, totaling 36 coins.
- Find out the number of nickels and dimes she possesses.
- The problem is set up to be solved with two equations, one for the number of coins, the other for the monetary value.
Example 4
- Kory drives from Edmonton to Lloydminster and back.
- The average speed going to Lloydminster is 96 km/h, and the return trip speed averages at 100 km/h.
- The total driving time amounts to 5.1 hours.
- The problem asks us to calculate the distance from Edmonton to Lloydminster.
- The problem is set up to be solved with two equations, one for the journey there, one for the return trip
Example 6
- James invests a total of $5000 in two different investments.
- The first investment yields 2.9% interest, while the second yields 4.5% interest.
- The total interest earned is $196.20.
- The problem involves figuring out how much James invested in each investment.
- The problem is set up to be solved with two equations, one for each investment.
Example 8
- A system of equations is: x + 2y = 0 and x + 5y = b.
- It has a solution with the coordinates (-2, a).
- The task would be to determine the values of a and b.
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