Assignment:
For the systems of linear equations in questions 1-3
- Determine how many solutions exist
- Use either elimination or substitution to find the solutions (if any)
- Graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection
Q1. 4x = 8 and 5y = 15
Q2. 0.2x + 0.4y = 1.7 and 8.3x - 6.3y = -4.3
Q3. x/3 - y/5 = 4 and 3x/4 + 2y/3 = 6
Q4. A man goes into a grocery store and buys a grapefruit and a toy ball. A 7% tax is applied to the price of non-food items. If the total bill is $5.15, including $0.18 in tax on the toy ball, what are the prices of the grapefruit and the ball?
Q5. On the first day of school, the percentage of boys in a particular class is 60%. During the school year, six girls move away, and are replaced in the class by six boys; this makes the class roster 75% boys. Find the number of boys and girls in the class on the first day of school.
Q6. Walt made an extra $9000 last year from a part-time job. He invested part of the money at a 9% annual rate of interest, and the rest at an 8% annual rate of interest. At the end of the year, he made a total of $770 in interest. How much was invested at 8%?
Q7. An express and local train leave Grays Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.
Q8. Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45. How many dimes does he have?
Provide complete and step by step solution for the question and show calculations and use formulas.