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Question 145910This question is from textbook Intermediate Algebra
: Will someone help me to solve the system of equations by using addition (elimination)method. If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is "no solution" or "infinitely many solutions.
2x – 7y = 3
-4x + 14y = -9
This question is from textbook Intermediate Algebra
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website! Will someone help me to solve the system of equations by using addition (elimination)method. If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is "no solution" or "infinitely many solutions.
2x – 7y = 3
-4x + 14y = -9
To make the y's cancel, multiply the top equation
through by 2: 4x - 14y = 6
4x - 14y = 6
-4x + 14y = -9
Now add vertically term by term:
4x - 14y = 6
-4x + 14y = -9
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0 = -3
All the variables canceled out and left a FALSE
numerical equation. Therefore there is no solution,
and the system is called "inconsistent".
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However if you had had this system of equations instead,
where there were a -6 where the -9 is:
2x – 7y = 3
-4x + 14y = -6
To make the y's cancel, you would, as above multiply the
top equation through by 2: 4x - 14y = 6
4x - 14y = 6
-4x + 14y = -6
Now as above, you would add vertically term by term:
4x - 14y = 6
-4x + 14y = -6
--------------
0 = 0
As above, all the variables canceled out, but this time
we are left with a TRUE numerical equation. Therefore
there are infinitely many solutions, and the system
is called "dependent".
Edwin
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