# Verify if the lines 2x-y+2=0 and x+y-4=0 are parallel.

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We have the two lines: 2x-y+2=0 and x+y-4=0.

Now each of them can be written in the slope and y-intercept format, y = mx + c, where m is the slope and c is the y-intercept..

2x-y+2=0

=> -y = -2x - 2

=> y = 2x + 2

Therefore the slope is 2

x+y-4=0

=> y = -x + 4

Here the slope is -1.

For the lines to be parallel they should have the same slope. This is not the case here.

**Therefore the two lines are not parallel.**

Given the lines :

2x - y + 2 = 0

x + y -4 = 0

We need to verify if the lines are parallel.

First. we need to rewrite the equations into the slope form y= ax+b

==> 2x - y + 2 = 0 ==> y= 2x + 2 ==> m1= 2

==> x + y - 4 = 0 ==> y= -x + 4 ==> m2= -1

**Then we notice that m1 and m2 are different. Then the lines are NOT parallel.**

To verify if the lines 2x-y+2=0 and x+y-4=0 are parallel.

Two lines a1x+b1y+c1= 0 and a2x+b2y+c2 are parallel if

a2/a1 = b2/b1. Or

b1/a1 = b2/a2.

In our case a1 = 2 , b1 = -1

a2 = 1, b2 = 1.

So b1/a1 = 1/2.

b2/a2 = 1/-1 = -1.

So b1/a1 = 1/2 is not equal to b2/a2 = -1.

So the given lines lines 2x-y+2=0 and x+y-4=0 are not ||.

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.**