Determine the intercepting point of the lines 3x 4y 11 x

Determine the intercepting point of the lines 3x + 4y = 11, -x + y = 11

The intercepting point of the given lines is the solution of the system formed by the equations of the lines.

We\'ll solve the system using substitution method:

-x + y = 11

We\'ll add x both sides:

y = 11 + x (1)

We\'ll substitute (1) in the first eq. of the system:

3x + 4(11 + x) = 11

We\'ll remove the brackets and we\'ll get:

3x + 44 + 4x = 11

We\'ll combine like terms form the left side:

7x + 44 = 11

We\'ll subtract 44:

7x = 11-44

7x = 33

We\'ll divide by 7:

x = -33/7

We\'ll plug in the value of y in (1):

y = 11 - 33/7

y = (77-33)/7

y = 44/7

The solution of the system represents the coordinates of the intercepting point of the lines: (-33/7 , 44/7).