1. What is a system of equations?
2. Solve for X and Y in the following problems. Show all your work.
a. X + Y= 10 , 3X + Y = 12
b. 2X + 5Y = 19 , 3X + 3Y = 15
c. 4X + Y = 22 , 2X + 3Y = 16
d. 12X + Y = 174 , 8X - 2Y = 36
3. Suppose Bob owns 2,000 shares of Company X and 10,000 shares of Company Y. The total value of Bob's holdings of these two companies is $372,000.
Suppose Frank owns 8,000 shares of Company X and 6,000 shares of Company Y. The total value of Franks holdings of these two companies is $400,000.
a. Write equations for Bob and Frank's holdings. Use the variables X and Y to represent the values of shares of Company X and Company Y.
b. Solve for the value of a share of Company X and Company Y. Show all your work.
4. Solve for X, Y, and Z in the following systems of three equations:
a. X + 2Y + Z = 22
X + Y = 15
3X + Y + Z = 37
b. 10X + Y + Z = 603
8X + 2Y + Z = 603
20X - 10Y - 2Z = -6
c. 22X + 5Y + 7Z = 12
10X + 3Y + 2Z = 5
9X + 2Y + 12Z = 14