Mathematics - coordinate geometry help !

The line L1 has a gradient 1/7 and passes through the point A(2,2).
The line ;L2 has a gradient -1 and passes through the point B(4.8)

the lines L1 and L2 intersect at the point c.


i have worked out the equations of L1 and L2 as:

L1 --> y= 1/7x + 12/7

L2 ----> Y= -X + 12

(both answers have been checked and are correct).


my question is :

Determine the coordinates of C

the answer to this is (9,3) but I am not sure how to work it out. Could anyone please answer it and also show their method?


thanks in advance

set the two equtions equal to each other and solve for x.

1/7 + 12/7 = - x + 12

x + 12 = - 7x + 84

8x = 72

x = 9

now replace y with 9 in one of the equations and solve for y

y = - x + 12

y = - 9 + 12

y = 3

so (9,3)