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What is the solution of the system x − 3y = –13 and 5x + 7y = 34? A. `x = (6)/(5)`, y = 4 B. `x = (7)/(2), y = (9)/(2)` C. `x = (1)/(2), y = (9)/(2)` D. x = –3, y = 7

User Psylosss
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2 Answers

4 votes

Answer:

C. X=1/2, Y=9/2

Explanation:

User Skubski
by
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3 votes

For this case we have the following system of equations:


x-3y = -13\\5x + 7y = 34

From the first equation we clear "x":


x = -13 + 3y

We substitute in the second equation:


5 (-13 + 3y) + 7y = 34

We apply distributive property:


-65 + 15y + 7y = 34

We add similar terms:


-65 + 22y = 34

We add 65 to both sides:


22y = 34 + 65\\22y = 99

We divide between 22 on both sides:


y = \frac {99} {22}\\y = \frac {9} {2}

We look for the value of the variable "x":


x = -13 + 3 \frac {9} {2}\\x = -13 + \frac {27} {2}\\x = \frac {-26 + 27} {2}\\x = \frac {1} {2}

Thus, the solution of the system is:


(x, y): (\frac {1} {2}, \frac {9} {2})

ANswer:


(x, y): (\frac {1} {2}, \frac {9} {2})

User Dreaming In Binary
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