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

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### 2 Answers

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)**

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)

We'll add (3) to (1):

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).**