We can solve the given system of linear equations like this:
1. Solve for one of the variables, for example, x from the first equation:
x - 6y = -13
x - 6y + 6y = -13 + 6y
x = -13 + 6y
2. Replace -13 + 6y for x into the second equation:
7x + 2y = 41
7(-13 + 6y) + 2y = 41
7×(-13) + 7×6y + 2y = 41
-91 + 42y + 2y = 41
-91 + 44y = 41
-91 + 44y + 91 = 41 + 91
44y = 132
44y/44 = 132/44
y = 3
By replacing 3 for y into x = -13 + 6y we can easily determine the value of x, then we get:
x = -13 + 6(3)
x = -13 + 18
x = 5
Then, the solution to the given system of equations is (5, 3).