Answer the question and solve the problems below. Make sure you show all your work so you can get partial credit even if you get the final answer wrong.
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Write My Essay For Me1. What is a system of equations?
A system of linear equations are two more equations that involve the same set of variables.
2. Solve for X and Y in the following problems. Make sure you show all your work so you can get partial credit even if your final answer is wrong.
a. X + Y= 10 , 3X + Y = 12
Eliminating Y
-X-Y=-10
+ 3X + Y = 12
____________
2X=2
X = 1
Substituting X=1 to obtain Y
1 + Y = 10
Y = 9
Answer: X=1, Y=9
b. 2X + 5Y = 19 , 3X + 3Y = 15
Simplifying 3X + 3Y = 15 by multiplying the equation by 1/3
X + Y = 5
Eliminating X
2X + 5Y = 19
+ -2X – 2Y = -10
________________
3Y = 9
Y = 3
Substituting to solve for X
X + 3 = 5
X = 2
Answer: X=2, Y=3
c. 4X + Y = 22 , 2X + 3Y = 16
Expressing Y in terms of X using the first equation
Y = 22 – 4X
Substituting this to equation 2 and solving for X.
2X + 3 (22 – 4X) = 16
2X + 66 – 12X = 16
-10X = -50
X = 5
Substituting to obtain Y
Y = 22 – 4(5)
Y = 22 – 20
Y = 2
Answer: X = 5 , Y = 2
d. 12X + Y = 174 , 8X – 2Y = 36
Expressing Y in terms of X using the first equation
Y = 174 – 12X
Substituting this to equation 2 and solving for X.
8X – 2(174 – 12X) = 36
8X – 348 + 24X = 36
32X = 384
X = 12
Substituting to obtain Y
Y = 174 – 12 (12)
Y = 174 – 144
Y = 30
Answer: X = 12, Y = 30
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 $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.
2000X + 10000Y = 372000
8000X + 6000Y = 400000
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.
Eliminating X
-8000X – 40000Y = -1488000
+ 8000X + 6000Y = 400000
-34000Y = -1088000
Y = 32
Substituting to solve for X
2000X + 10000 (32) = 372000
2000X + 320000 = 372000
2000X = 372000 – 320000
2000X = 52000
X = 26
Answer: A share of company X is $26 and a share of company Y is $32.
3. 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
Eliminating Z using equations 1 and 3
-X – 2Y – Z = -22
+) 3X + Y + Z = 37
________________
2X – Y = 15
Using the equation above and equation 2 to eliminate Y and solve for X
2X – Y = 15
+) X + Y = 15
________________
3X = 30
X = 10
Substituting X=10 to solve for Y
10 + Y = 15
Y = 5
Substituting X = 10 and Y = 5 to solve for Z
10 + 2(5) + Z = 22
20 + Z = 22
Z = 2
Answer: X= 10, Y=5, Z=2
b. 10X + Y + Z = 603
8X + 2Y + Z = 603
20X – 10Y – 2Z = -6
Eliminating Z using eq 1 and 2
10X + Y + Z = 603
+) -8X – 2Y – Z = -603
2X – Y = 0 or 2X = Y
Eliminating Z using eq 1 and ½ * eq3
10X + Y + Z = 603
+) 10X – 5Y – Z = -3
20X – 4Y = 600
(simplifying above by multiplying ¼ to the equation)
5X – Y = 150
Solving for X by substituting 2X = Y
5X – 2X = 150
3X = 150
X = 50
Solving for Y
2 (50) = Y
Y = 100
Solving for Z
10(50) + 100 + Z = 603
Z = 603 – 600
Z = 3
Answer: X = 50, Y = 100, Z = 3
c. 22X + 5Y + 7Z = 12
10X + 3Y + 2Z = 5
9X + 2Y + 12Z = 14
Eliminating Z using eq 2 and eq 3
-60X – 18Y – 12Z = -30
+) 9X + 2Y + 12Z = 14
-51X – 16Y = -16
Eliminating Z using eq1 and eq2
44X + 10Y + 14Z = 24
+)-70X – 21Y – 14Z = -35
-26X – 11Y = -11
Eliminating Y to solve for X
-51(11)X – 16(11)Y = -16(11)
+) 26(16)X + 11(16)Y = 11(16)
(-51(11)+26(16))X = 0
X = 0
Solving for Y
-26(0) + -11Y = -11
Y = 1
Solving for Z
10(0) + 3(1) + 2Z = 5
3 + 2Z = 5
2Z = 2
Z = 1
Answer: X=0, Y = 1, Z=1
Assignment Expectations
- Define a system of equations.
- Solve systems of equations with two and three variables.
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