It does, x=7/11 and y=68/33
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The work-out, showing every step (when you've done enough of these some steps can be combined, especially the simpifications that come later):
x + 6y = 13 (1)
y = (5/3)x + 1 (2)
One approach is to substitute the right hand side (RHS) of eq (2) for "y" in eq (1), call this new version "eq 1a":
x + 6((5/3)x + 1) = 13 (1a)
The reason for doing that is now we have one equation and one unknown x, and we should be able to solve for x:
Continuing to solve (1a) for x, we bring the 6 inside the paren's:
x + ((30/3)x + 6) = 13
x + 10x + 6 = 13
combine the x and 10x:
11x + 6 = 13
subtract 6 from both sides
11x + 6 - 6 = 13 - 6
simplify
11x = 7
divide both sides by 11
11x/11 = 7/11
simplify
x = 7/11 ---> plug this value of x into (2) to get y:
y = (5/3)(7/11) + 1 = 35/33 + 33/33 = 68/33
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Check using (1):
7/11 + 6(68/33) = 7/11 + 408/33 = 21/33 + 408/33 = 429/33 = 13 (ok)