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

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

At the point of intersection of the lines the x and y co-ordinates are the same

We have y = -x +14 and y = 4x - 11.

Equating the y-coordinates ,we get

-x + 14 = 4x - 11

=> 5x = 25

=> x = 5

y = -x + 14 = -5 + 14 = 9

The point of intersection of the two lines is ( 5, 9)

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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).