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

For this case we have the following system of equations:[tex]x-3y = -13\\5x + 7y = 34[/tex]From the first equation we clear "x":[tex]x = -13 + 3y[/tex]We substitute in the second equation:[tex]5 (-13 + 3y) + 7y = 34[/tex]We apply distributive property:[tex]-65 + 15y + 7y = 34[/tex]We add similar terms:[tex]-65 + 22y = 34[/tex]We add 65 to both sides:[tex]22y = 34 + 65\\22y = 99[/tex]We divide between 22 on both sides:[tex]y = \frac {99} {22}\\y = \frac {9} {2}[/tex]We look for the value of the variable "x":[tex]x = -13 + 3 \frac {9} {2}\\x = -13 + \frac {27} {2}\\x = \frac {-26 + 27} {2}\\x = \frac {1} {2}[/tex]Thus, the solution of the system is:[tex](x, y): (\frac {1} {2}, \frac {9} {2})[/tex]ANswer:[tex](x, y): (\frac {1} {2}, \frac {9} {2})[/tex]