Unit 5 Study Guide (Systems of Equations) 8th Grade Math

1.Larry and his friends went to the concession stand and bought drinks, d, for $1 and slices of pizza, p, for $1.75. The total cost for 9 items was $13.50. Write a system of equations to represent the situation and find out how many drinks and slices of pizza they bought.

• d + p = 9 and 1.75p = 13.50

• d + p = 9 and d + 1.75p = 13.50

• d + p = 13.50 and 1.75p = 9

• d + 1.75p = 9 and d + p = 13.50

2.At a school fundraiser candles, c, and wrapping paper, w, were being sold. Carlos sold 12 candles and 10 wrapping papers for a total of $226. Marie sold 5 candles and 15 wrapping papers for a total of $186.25. Which of the following systems of equations will help to solve for the cost of each candle and each wrapping paper?

• 12c + 10w = 226, 5c + 15w = 186.25

• 12c + 10w = 186.25, 5c + 15w = 226

• 10c + 12w = 226, 15c + 5w = 186.25

• 15c + 5w = 226, 10c + 12w = 186.25

3. 3.The system of equations is given. -8y = -16 + 2x 8 - 3x = -4y Which graph shows the solution for the system of equations?

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4.Which graph shows the solution (3,-2)?

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5. Consider the partial system of equations.
5x+5y = 15 and _______
If paired with each of the following, would it cause the system to have zero, one, or infinite number of solutions?

10x - 10y = 15

• Zero (No Solution)

• One Solution

• Infinite Solutions

5. Consider the partial system of equations.
5x+5y = 15 and _______
If paired with each of the following, would it cause the system to have zero, one, or infinite number of solutions?

x+y=3

• Zero (No Solution)

• One Solution

• Infinite Solutions

5. Consider the partial system of equations.
5x+5y = 15 and _______
If paired with each of the following, would it cause the system to have zero, one, or infinite number of solutions?

x+y=5

• Zero (No Solution)

• One Solution

• Infinite Solutions

6. Emilee has $6.80 to spend on number candles and birthday candles for her mom’s birthday cake. She thinks she will purchase a total of 50 candles. The system of equations representing this scenario is shown. n+b = 50 1n + .10b = 6.80 How many of each candle can she buy?

• 2 number candles and 48 birthday candles

• 48 number candles and 2 birthday candles

• 20 number candles and 30 birthday candles

• 15 number candles and 35 birthday candles

7.The Franco family have to order candles for their wedding decorations. They want x “single wick candles” and y “3 wick candles”. They have $350 to spend on all the candles. The cost of "single wick candles" is $10 and “3 wick candles” cost $15. They want the total amount of single wick candles to be 10 greater than 3 wick candles. They use the equations 15x + 10y = 350 and x+10 = y. Are these equations set up correctly?

• Only the first equation is correct

• Only the second equation is correct

• Neither equation is correct

• Both Equations are correct

8.Based on the given system of equations, how many single wick and how many 3 wick candles were purchased?

• 10 single wick and 5 three wick candles

• 5 single wick and 10 three wick candles

• 20 single wick and 10 three wick candles

• 10 single wick and 20 three wick candles