Solving System of Equations Exercises

Substitution Method

For the following exercises, determine whether the given ordered pair is a solution to the system of equations.

1. For the following exercises, solve each system by substitution.

2. For the following exercises, solve each system by addition.

3. For the following exercises, solve each system by any method.

4. Graphical

5. For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has one solution, no solution, or infinite solutions. Real-World Applications For the following exercises, solve for the desired quantity.

6. The top band in the state charges , where x is the total  number of attendees at the concert. The venue charges $70 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point? For the following exercises, use a system of linear equations with two variables and two equations to solve.

7.The startup cost for a boutique is $15,000, and each floral arrangement costs $17 for the boutique to make. If each arrangement is then sold for $25, after how many arrangements does the boutique break even?

8.If a scientist mixed 15% saline solution with 48% saline solution to get 20 gallons of 35% saline solution, how many gallons of 15% and 48% solutions were mixed? Round each to the nearest whole gallon.

9.Admission into an amusement park for 4 children and 2 adults is $133.50. For 6 children and 4 adults, the admission is $235.50. Assuming a different price for children and adults, what is the price of the child ticket and the price of the adult ticket?