Systems of Linear Equations Worksheets Grade 10

1. A triangular region is bounded by the lines y = 2x + 1, y = -3x + 11, and the x-axis. Visualize this triangle formed by these three lines on a coordinate plane. What is the area of this triangular region?
2. 4x + 6y = 48; 2x - 8y = -20; x = ?
3. 5x + 3y = 41; 3x - 5y = 11; x = ?

…and 5 more problems

1. Olivia is a concert promoter organizing two types of VIP packages for an upcoming tour. The Gold package requires 3 hours of backstage setup and 1 hour of soundcheck coordination, while the Platinum package requires 5 hours of backstage setup and 3 hours of soundcheck coordination. Due to venue constraints, Olivia has exactly 63 hours available for backstage setup and 33 hours available for soundcheck coordination across all packages. If she wants to use every available hour, how many of each VIP package should she offer?
2. Liam is managing a small business that produces two types of artisanal candles: lavender and sandalwood. The lavender candles sell for $12 each, and the sandalwood candles sell for $15 each. Last weekend, Liam sold 40 candles in total and collected $540 in revenue. How many lavender candles did Liam sell?
3. Liam is managing a small business that produces two types of handmade candles: lavender and sandalwood. The lavender candles require 2 ounces of wax and 0.5 ounces of fragrance oil each, while the sandalwood candles require 3 ounces of wax and 0.25 ounces of fragrance oil each. If Liam has 48 ounces of wax and 9 ounces of fragrance oil available, how many of each type of candle should he make to use all available supplies?

…and 4 more problems

1. A tech company is analyzing the relationship between their advertising budget and quarterly revenue. They found that when they spend $x$ thousand dollars on digital ads and $y$ thousand dollars on print ads, their revenue follows the system: 3x + 2y = 24 (in thousands) for digital and print ads respectively. Additionally, they discovered that doubling the digital ad budget while maintaining the same print budget increases revenue by $8,000. Determine the advertising budgets (in thousands) that satisfy both conditions.
2. Aroha and Tane are planning a school fundraising event. They are selling two types of raffle tickets: standard tickets and premium tickets. A standard ticket costs $12, and a premium ticket costs $18. On the first day of sales, they sold 28 more premium tickets than standard tickets, and the total revenue from both types of tickets was $1,584. Kaia, the school treasurer, needs to know exactly how many standard tickets and how many premium tickets were sold. How many of each type were sold?
3. A technology company is analyzing the profitability of two different software subscription plans. The Basic plan costs $15 per month with no setup fee, while the Premium plan costs $25 per month with a one-time $50 setup fee. After how many months will the total cost of both plans be equal?

…and 4 more problems