Parallel lines.Find if the lines 2x-y+2=0 and x+y-4=0 are parallel

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Two lines are parallel if they have the same slope.

For the lines 2x-y+2=0 and x+y-4=0, the slope is :

2x - y + 2 = 0

=> y = 2x + 2

slope  = 2

x + y - 4 = 0

=> y = -x - 4

slope  = 1

The two lines have different slopes, so they  are not parallel.

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

2x-y+2=0 and x+y-4=0

Recall that parallel lines have the same slope. Rewrite the two equations in point slope form: 

y = mx + b where m is the slope. 

2x-y+2=0 

(1)    y = 2x + 2

x + y - 4 = 0

(2)    y = x + 4

Equation (1) has a slope of 2 and equation (2) has a slope of 1. Since the slopes are not equal, they are not parallel. 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll solve the system formed of the given equations of the lines and we'll check if it has solutions. If the system has no solutions, that means that the lines are not intercepting each other, so they are parallel.

We'll solve the system using substitution method. We'll change the 2nd equation into:

x+y = 4

x = 4 - y (3)

We'll substitute (3) in (1):

2(4 - y) - y = -2

We'll remove the brackets:

8 - 2y - y = -2

We'll combine like terms and we'll subtract 8 both sides:

-3y = -2 - 8

-3y = -10

We'll divide by -3:

y = 10/3

We'll substitute y in (3):

x = 4 - 10/3

x = (12-10)/3

x = 2/3

The solutions of the system is: {2/3 ; 10/3}.

Since the system has a solution, that means that the lines are not parallel.

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