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

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krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

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)

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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).

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