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]
