Determine the point of intersection of the lines y=-x+14 and y=4x-11?

To determine the intercepting point of the given lines,
we'll have to solve the system of equations of the
lines.

We'll re-write the equations, keeping the variables
x and y to the left side.

In the first equation, we'll
shift x to the left, changing it's sign:

x + y = 14
(1)

In the second equation, we'll shift x to the left and
we'll re-arrange the terms:

4x - y = 11
(2)

We'll solve the system using
substitution:

x = 14 - y
(3)

We'll replace x in the 2nd equation by the expression
from (3):

4(14 - y) - y =
11

We'll remove the
brackets:

56 - 4y - y = 11

-5y
= 11 - 56

-5y = -45

We'll
divide by -5:

y = 9

We'll
substitute y in (3):

x = 14 -
9

x = 5

The
solution of the system represents the intercepting point of the lines, whose coordinates
are given by the pair: (5 ; 9).