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How do you solve linear equations?

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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

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This solution explains the steps for solving the linear equations with calculations and answers in 940 words in an attached Word document.

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