Day 18 - Solving simple systems

A system of equations is a set of two or more equations considered together. A solution to a system of equations in two variables is an ordered pair that is a solution to every equation in the system.

1. Is (2, −1) a solution to the system 2𝑥+𝑦=3 𝑥+𝑦=1 ? YES

2. Is (1, -3) a solution to the system 3𝑥+2𝑦=−3 𝑥−3𝑦=6 ? NO

3. Solve by graphing 2𝑥+𝑦=3 𝑥+𝑦=1

3. Solve by graphing 2𝑥+𝑦=3 𝑥+𝑦=1 What is the point of intersection of the two graphs? What is the solution to the system of equations?

What is the relationship between the point(s) of intersection and the solution(s) to the system of equations? They are the same point.

Bank Accounts Thomas has been offered a job where he can earn $5 for every hour he spends painting houses. If he starts with nothing in his bank account and doesn't spend any money all week, how much will be in his bank account?

Bank Accounts - Answer The answer depends on how many hours Thomas works. If "h" represents the number of hours he works and "a" represents the amount of money in his bank account, we know that a = 5h.

Bank Accounts - Again Suppose now that Thomas has an alternate job offer in which he would be given an initial payment of $12 and then would earn $3 an hour? Which job would give Thomas the most money after 10 hours?

Bank Accounts - Answer After 10 hours, the first job would give him 5 ×10 = $50 and the second job would give him only 3 × 10 + 12 = $42.

Bank Accounts - Time Complete the table for the first equation, a = 5h Complete the table for the second equation, a = 3h + 12 ℎ 1 2 3 4 5 6 7 8 9 𝑎 ℎ 1 2 3 4 5 6 7 8 9 𝑎

Bank Accounts - Time Table for the first equation, a = 5h The table for the second equation, a = 3h + 12 ℎ 1 2 3 4 5 6 7 8 9 𝑎 10 15 20 25 30 35 40 45 ℎ 1 2 3 4 5 6 7 8 9 𝑎 12 15 18 21 24 27 30 33 36 39

Bank Accounts - Time 𝑎=3ℎ+12 a=5h