Create System 2 Equations & 2 Variables
Sarah buys 3 notebooks and 2 pencils for $14. Her friend Tom buys 2 notebooks and 4 pencils for $16. How much does each notebook and pencil cost?
Let x = cost of a notebook
Let y = cost of a pencil
Write a system of two equations representing this situation.
First equation: 3x + 2y = 14
Second equation: 2x + 4y = 16
Solve the system of equations:
x + y = 7
x - y = 3
Answer:
- Solve by adding the equations
- (x + y) + (x - y) = 7 + 3
- 2x = 10
- x = 5
- Substitute x = 5 into x + y = 7
- 5 + y = 7
- y = 2
- Solution: (x, y) = (5, 2)
Graph the equations y = x + 2 and y = -x + 6, and determine the point of intersection.
*Answer:*
- Plot the first line by finding points (0, 2) and (4, 6)
- Plot the second line by finding points (0, 6) and (6, 0)
- The point of intersection is (2, 4)
- Solution: (x, y) = (2, 4)
Determine the number of solutions for the system:
2x + y = 4
x - y = 1
Answer: One unique solution (x = 1.5, y = 1)
Who is often credited with creating the viral "Renegade" dance on TikTok?
Answer: Jalaiah Harmon, a teenage dancer who originally choreographed the dance that became a global phenomenon in 2019-2020.
A local movie theater sells adult tickets for $12 and child tickets for $8. On a particular day, the theater sold a total of 50 tickets, and the total revenue was $480. How many adult and child tickets were sold?
Let x = number of adult tickets
Let y = number of child tickets
Write a system of two equations representing this situation.
First equation: x + y = 50
Second equation: 12x + 8y = 480
Solve the system of equations:
2x + y = 5
x - y = 2
Answer:
- Use substitution method
- From x - y = 2, rearrange to x = y + 2
- Substitute into 2x + y = 5
- 2(y + 2) + y = 5
- 2y + 4 + y = 5
- 3y = 1
- y = 1/3
- Substitute y = 1/3 back into x = y + 2
- x = 1/3 + 2
- x = 7/3
- Solution: (x, y) = (7/3, 1/3)
Solve the system of equations graphically:
y = 2x
y = -x + 6
*Answer:*
- Plot y = 2x line passing through (0, 0) and (3, 6)
- Plot y = -x + 6 line passing through (0, 6) and (6, 0)
- The point of intersection is (2, 4)
- Solution: (x, y) = (2, 4)
How many solutions exist in this system?
3x + 2y = 66x + 4y = 13
Answer: Zero solutions (inconsistent system - lines are parallel but do not intersect)
What is the name of the TikTok star who became famous for her "Clean Girl" aesthetic and makeup tutorials?
Answer: Alix Earle, who gained massive popularity for her get-ready-with-me (GRWM) videos and lifestyle content.
A bicycle manufacturer produces two types of bikes: mountain bikes and road bikes. Each mountain bike requires 6 hours of labor and 4 yards of material, while each road bike requires 4 hours of labor and 5 yards of material. If the factory has 72 labor hours and 100 yards of material available, how many of each type of bike can be produced?
Let x = number of mountain bikes
Let y = number of road bikes
Write a system of two equations representing this situation.
First equation: 6x + 4y = 72
Second equation: 4x + 5y = 100
Solve the system of equations:
3x + 2y = 13
2x - y = 4
Answer:
- Use elimination method
- Multiply second equation by 2
- 3x + 2y = 13
- 4x - 2y = 8
- Add equations to eliminate y
- 7x = 21
- x = 3
- Substitute x = 3 into 3x + 2y = 13
- 3(3) + 2y = 13
- 9 + 2y = 13
- 2y = 4
- y = 2
- Solution: (x, y) = (3, 2)
Graphically solve the system of equations:
2x + y = 5
x - y = 1
*Answer:*
- For 2x + y = 5, find points (0, 5) and (2.5, 0)
- For x - y = 1, find points (0, -1) and (1, 0)
- Carefully plot both lines
- The point of intersection is (2, 1)
- Solution: (x, y) = (2, 1)
Find the number of solutions for:
x + 2y = 52x + 4y = 10
Answer: Infinitely many solutions (lines are identical/overlapping)
Which TikTok creator launched the popular makeup and skincare brand "Relevant: Your Skincare" in 2022?
Answer: Meredith Duxbury, a beauty and lifestyle influencer known for her makeup transformation videos.
A small bakery makes two types of pastry boxes: deluxe and standard. A deluxe box contains 6 cookies and 4 muffins, while a standard box contains 3 cookies and 5 muffins. If the bakery wants to create a total of 72 pastry boxes with exactly 300 total items (cookies and muffins combined), how many of each type of box should they make?
Let x = number of deluxe boxes
Let y = number of standard boxes
Write a system of two equations representing this situation.
First equation: x + y = 72
Second equation: 6x + 3y = 300
Solve the system of equations:
2x + 3y = 11
3x - 2y = 4
Answer:
- Use elimination method
- Multiply first equation by 3 and second by 2
- 6x + 9y = 33
- 6x - 4y = 8
- Subtract equations to eliminate x
- 13y = 25
- y = 25/13
- Substitute y = 25/13 into 2x + 3y = 11
- 2x + 3(25/13) = 11
- 2x + 75/13 = 11
- 2x = 11 - 75/13
- 2x = (143 - 75)/13
- 2x = 68/13
- x = 34/13
- Solution: (x, y) = (34/13, 25/13)
Solve the following system graphically, identifying the special characteristic of the lines:
y = 0.5x + 1
y = 0.5x - 3
*Answer:*
- Both lines have the same slope (0.5)
- Plot the first line through points (0, 1) and (4, 3)
- Plot the second line through points (0, -3) and (4, -1)
- The lines are parallel and do not intersect
- No solution exists (inconsistent system)
Analyze this system and determine solution count:
2x - y = 34x - 2y = 5
Answer: Zero solutions (inconsistent system - lines are parallel but do not intersect)
What was the legal dispute between TikTok star Bryce Hall and which content house that led to his temporary ban from the platform?
Answer: Bryce Hall was temporarily banned from the Sway House, a content creator collective managed by TalentX Entertainment, following various controversies and internal conflicts.
An investment firm is allocating funds between two different investment portfolios: a low-risk portfolio yielding 5% annually and a high-risk portfolio yielding 12% annually. The firm wants to invest a total of $500,000 and aims to generate $47,000 in annual returns. How much should they invest in each portfolio?
Let x = amount invested in low-risk portfolio
Let y = amount invested in high-risk portfolio
Write a system of two equations representing this situation.
First equation: x + y = 500,000
Second equation: 0.05x + 0.12y = 47,000
Solve the system of equations:
5x + 4y = 17
2x - 3y = -4
Answer:
- Use elimination method
- Multiply first equation by 2 and second by 5
- 10x + 8y = 34
- 10x - 15y = -20
- Subtract equations to eliminate x
- 23y = 54
- y = 54/23
- Substitute y = 54/23 into 5x + 4y = 17
- 5x + 4(54/23) = 17
- 5x + 216/23 = 17
- 5x = 17 - 216/23
- 5x = (391 - 216)/23
- 5x = 175/23
- x = 35/23
- Solution: (x, y) = (35/23, 54/23)
Solve this system graphically with fractional coefficients:
2x + 3y = 12
3x - y = 5
*Answer:*
- For 2x + 3y = 12, find points (0, 4) and (6, 0)
- For 3x - y = 5, find points (0, -5) and (5/3, 0)
- Carefully plot both lines
- The point of intersection is (3, 2)
- Solution: (x, y) = (3, 2)
- Verify by substituting into both original equations
Solve and identify solutions for:
x + y = 62x + 2y = 12
Answer: Infinitely many solutions (lines are identical/overlapping)
Name the TikTok creator who successfully transitioned to a major record deal after going viral with their original music on the platform, and identify their breakthrough song.
Answer: Tai Verdes, who went viral with his song "Stuck in the Middle" in 2020. He gained popularity through TikTok and subsequently signed with Arista Records, launching his music career.