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

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The point of intersection of the two lines will satisfy the equations of both the lines. Therefor this point can be found by solving the equation of lines for x and y.

Given equation of lines are:

3x + 4y = 11 ... (1)

-x + y = 11 ... (2)

Multiplying equation (2) by 3:

-3x + 3y == 33 ... (3)

Adding equations (1) and (3):

3x - 3x + 4y + 3y = 11 + 33

==> 7y = 44

==> y = 44/7

Substituting this value of y in equation (2):

-x + 44/7 = 11

==> x = 44/7 - 11 = - 33/7

Answer:

Point of intersection is (-33/7, 44/7)

3x+4y =11.....(1)

-x+y = 11...........(2)

We solve the equations for x and y. The solutions in x and y are the coordinates of the interction point.

Eq(1)+3*eq(2) eliminates x:

4y+3y = 11+3*11 = 44

7y = 44.

y = 44/7.

Substitute y = 44/7 in (2):

-x+44/7 = 11

-11+44/7 = x

(-77+44)/7 = x

-33/7 = x.

So x= -33/7 and y = 44/7

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).**