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# Solve problems for Systems of linear equations

1. Solve for X and Y in the following problems. Make sure you show all your work.

a. X + Y=7 , X + 2Y = 11

b. 3X + 7Y = 24, 9X + 5Y = 24

c. 4X + Y = 17, 2X + 3Y = 21

d. 18X + Y = 42, 6X - 3Y = -6

2. 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 \$340,000.

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 \$340,000.

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 your work so you can get partial credit even if your final answer is wrong.

3. Solve for X, Y, and Z in the following systems of three equations:

a. X + Y + 2Z = 5

X + Y = 5

X + 3Y + Z = 11

b. X + 10Y + Z = 52

5X + Y + 4Z = 15

X + 2y - 3Z = 12

c. 22X + 5Y + 7Z = 12

10X + 3Y + 2Z = 5

9X + 2Y + 12Z = 14

#### Solution Preview

1A: X=7-Y, X=11-2Y
7-Y=11-2Y
2Y-Y=11-7
Y=4
X=7-4
X=3

1B: 3X=24-7Y, 9X=24-5Y
(3X=24-7Y)*3 9X=72-21Y
72-21Y=24-5Y
72-24=21Y-5Y
48=16Y
(48=16Y)/16
3=Y
3X=24-7*3
3X=24-21
3X=3
(3X=3)/3
X=1

1C: 4X=17-Y, 2X=21-3Y
(2X=21-3Y)*2 4X=42-6Y
17-Y=42-6Y
6Y-Y=42-17
5Y=25
(5Y=25)/5
Y=5
4X=17-5
4X=12
(4X=12)/4
X=3

1D: 18X=42-Y, 6X=-6+3Y
(6X=6+3Y)*3 18X=-18+9Y
42-Y=-18+9Y
42+18=Y+9Y
60=10Y
(60=10Y)/10
6=Y
18X=42-6
18X=36
(18X=36)/18
X=2

2: Let X the value of each share of Company X
Let Y the value of each share of ...

#### Solution Summary

This solution shows step-by-step calculations to solve systems of linear equations.

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