Systems and Equations
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1. What is a system of equations?
2. Solve for X and Y in the following problems using either substitution or elimination methods. 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
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 your work so you can get partial credit even if your final answer is wrong.
4. Solve for X, Y, and Z in the following systems of three equations using either substition or elimination methods:
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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Solution Summary
Systems and Equations are assessed.
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1. What is a system of equations?
A system of equations is a collection of two or more equations with a same set of unknowns.
2. Solve for X and Y in the following problems using either substitution or elimination methods. 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
if we multiply 2nd equation by -1;
X + Y = 10
-3X - Y = -12
now add them together;
X-3X+Y-Y=10-12
-2X=-2
X=1
and now we can find Y from either one of the equations by substituting X=1;
1+Y=10
Y=9
b. 2X + 5Y = 19 , 3X + 3Y = 15
from the first equation;
2X=(19-5Y)
X=(19-5Y)/2
substitude X in 2nd equation;
3(19-5Y)/2+3y=15
(57-15Y)/2+6Y/2=15
(57-15Y+6Y)/2=15
57-9Y=30
9Y=27
Y=3
and solve for X;
3X+3(3)=15
3X=15-9
3X=6
X=2
c. 4X + Y = 22 , 2X + 3Y = 16
mutiply 2nd equation by -2;
4X + Y = 22
-4X ...
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