System of Linear Equations
Solve for X and Y in the following problems. Make sure you show all your work.
X + Y=7, X + 2Y = 11
y
y + 2y = 11
y = 4
3X + 7Y = 24, 9X + 5Y = 24
7/3y
7/3 y) + 5y = 24
63/3y + 5y = 24
y = 3
4X + Y = 17, 2X + 3Y = 21
y = 17 -- 4x
2x + 3(17-4x) = 21
+ y = 17
y = 5
18X + Y = 42, 6X - 3Y = -6
y = 42 -- 18x
+ y = 42
y = 6
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.
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.
2000X + 10000Y = 340,000
8000X + 6000 Y = 340,000
Solve for the value of a share of Company X and Company Y. Show your work.
2000x = 340,000 -- 10000y
x = 170 -- 5y
8000 (170 -- 5y) + 6000y = 340,000
1,360,000 -- 40,000y + 6000y = 340,000
-34,000y = -1020000
y = 30
2000x + 300000 = 340,000
2000x = 40,000
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
z = 11 -- x -- 3y
x = 5 -- y
(5 -- y + y + 2(11-x-3y) = 5
5 + 22 -- 2x -- 6y = 5
27 -- 2 (5-y) -- 6y = 5
27 -- 10 + 2y -- 6y = 5
17 -- 4y = 5
-4y = -12
y = 3
z = 0
b. X + 10Y + Z = 52
5X + Y + 4Z = 15
X + 2y - 3Z = 12
-5x -- 50 y -- 5z = -260
5x + y + 4z = 15
-49y -- 1z = -245
x + 10 y + z = 52
-x -2y + 3z = -12
8 y + 4 z = 40
4z = 40 -- 8y
z = 10 -- 2y
-49 y -- (10 -- 2y) = -245
-47y + 2y = -235
y=5
8y+4z=40
z = 0
x + 50 + 0 = 52
c. 22X + 5Y + 7Z = 12
10X + 3Y + 2Z = 5
9X + 2Y + 12Z = 14
66x + 15 y + 21z = 36
-50x -- 15y -- 10z = -25
16x +11z = 11
20 x + 6 Y + 4 Z = 10
-27x - 6 y -- 36z = -42
-7x -32z = -32
16x = 11 -- 11z
x = (11 -- 11 z) / 16
-7 (11/16 -- 11/16z) - 32z = -32
11/16 -- 11/16z + 4.5714z = 4.5714
3.8839 z = 3.8839
z = 1
16 x + 11 = 11
0 + 3y + 2 = 5
3y = 3
y = 1
