Question 16303: find the variables
3x+4y-3c=5
x+6y+2c=3
6x+2y+3c=4
Please help me out this with step by step solution
thanks
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website!
find the variables
3x+4y-3c=5
x+6y+2c=3
6x+2y+3c=4
`
1. Does any of the three equations contain only two letters?
2. If the answer to 1 is yes, choose that letter to eliminate first.
3. If the answer to 1 is no, choose any of the three letters to eliminate first.
4. Choose a pair of equations that contains the letter to eliminate first.
5. Eliminate that letter from the pair of equations chosen in 4.
6. If the answer to 1 was yes, solve the system of two equations and one
unknown consisting of the original equation that contained only two letters and
the resulting equation from 5 for those two letters.
7. If the answer to 1 was no, choose a different pair of equations from the pair chosen in 4, and eliminate the letter chosen in step 3.
8. If the answer to 1 was no, solve the system of two equations and two
unknowns from steps 5 and 7
9. Choose any one of the original equations that contains the letter that was
eliminated first.
10. Substitute the values of the two variables found in step 6 or step 7
11. Solve for the variable eliminated first.
`
3x+4y-3c=5
x+6y+2c=3
6x+2y+3c=4
`
`
1. Does any of the three equations contain only two letters?
`
The answer is no. So go on to step 2
`
2. If the answer to 1 is yes, choose that letter to eliminate first.
`
The answer to 1 was no, so go on to step 3
`
3. If the answer to 1 is no, choose any of the three letters to eliminate first.
`
Choose c.
`
4. Choose a pair of equations that contains the letter to eliminate first.
`
Choose 1 and 3.
`
5. Eliminate that letter from the pair of equations chosen in 4.
`
3x + 4y - 3c = 5
6x + 2y + 3c = 4
`
Add these two vertically term by term and the c terms cancel
`
9x + 6y = 9
`
6. If the answer to 1 was yes, solve the system of two equations and one
unknown consisting of the original equation that contained only two letters
and the resulting equation from 5 for those two letters.
`
The answer to 1 was no, so go on to step 7
`
7. If the answer to 1 was no, choose a different pair of equations from the
pair chosen in 4, and do step 5.
`
Choose the first and second equations:
`
3x + 4y - 3c = 5
`x + 6y + 2c = 3
`
We must eliminate c. Multiply the first equation through by 2, and the second
equation through by 3 and add vertically term by term:
`
6x + 8y - 6c = 10
3x + 18y + 6c =` 9
-------------------
9x + 26y ` ` `= 19
`
8. If the answer to 1 was no, solve the system of two equations and two unknowns from steps 5 and 7.
`
9x +` 6y =` 9
9x + 26y = 19
`
Multiply the first equation by -1 and add them vertically term by term:
`
-9x - `6x = -9
`9x + 26y = 19
---------------
` ` ` 20y = 10
` ` ` ` y = 1/2
`
Substitute 1/2 for y in the first equation 9x + 6y = 9
`
9x + 6(1/2) = 9
9x + 3 = 9
9x = 6
`x = 6/9 = 2/3
`
9. Choose any one of the original equations that contains the letter that was
eliminated first.
`
Choose the second original equation, x + 6y + 2c = 3
`
10. Substitute the values of the two variables found in step 6 or step 7
`
We substitute 2/3 for x and 1/2 for y
`
x + 6y + 2c = 3
(2/3) + 6(1/2) + 2c = 3
`
11. Solve for the variable eliminated first
`
2/3 + 3 + 2c = 3
` ` ` ` ` 2c = -2/3
` ` ` ` ` `c = -1/3
`
Edwin
AnlytcPhil@aol.com
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