Question 78377
Solution by substitution:

x + 4y = 13
==> x = 13 -4y ------------------(i)
Plugging in this value of x in the first equation, we get,
4(13-4y) - 6y = -14
==> 52 - 16y - 6y = -14
==> 52 - 22y = -14
adding -52 to both sides,
-22y = -14 -52
==> -22y = -66
==> -22y/22 = -66/22
==> y = 3
Putting this value in (i), x = 13 -4(3)
                             = 13 - 12
                             = 1

Thus x = 1 and y = 3

Solution by elimination:

4x - 6y = -14----------------------(1)
x + 4y = 13 ----------------------(2)

==> 4x + 16y = 52 -----------(2) x 4
    4x - 6y = - 14 -------------(1)
Subtracting the two equations we get,

16y + 6y = 52 + 14
==> 22y = 66
==> 22y/22= 66/22
==> y = 3
Plugging in this in (2), x = 13 - 4y

                           = 13 - 4(3)
                           = 13 - 12
                           = 1

Thus x = 1, y = 3