Verify if the line x=42-14y intersects the line y=2x-11.

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have the line x = 42 - 14y. The other line is y = 2x - 11.

Use x = 42 - 14y from the equation of the first line and substitute in the second

y = 2x - 11

=> y = 2( 42 - 14y) - 11

=> y = 84 - 28y - 11

=> y = -28y + 73

=> 29y = 73

=> y = 73/29

x = 42 - 14 * ( 73/29)

=> x = 196/29

Therefore, the lines do intersect and the point of intersection is (196/29 , 73/29)

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine if the lines are intercepting each other, we'll have to solve the system formed form the equations of the lines and to see if it has a solution. The solution of the system represents the intercepting point of the lines.

We'll change the 1st equation in:

x+14y=42 (1)

We'll change the 2nd equation in:

2x-y=11  (2)

We'll solve the system using elimination method. For this reason, we'll multiply (2) by 14:

28x - 14y = 154 (3)

28x - 14y +  x + 14y = 154 + 42

We'll eliminate like terms:

29x = 196

We'll divide by 29:

x = 196/29

We'll susbtitute x in (1) and we'll get:

196/29 + 14y=42

We'll subtract 196/29 both sides:

14y = 42 - 196/29

14y = (1218-196)/29

We'll divide by 14:

y = 1022/406

The lines are intercepting and the coordinates of the intercepting point are: (196/29, 1022/406).