# What is the point of intersection ( if any) of the lines y+x -2 = 0 and 2y-4x +5 = 0 ?

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Given the lines:

y + x -2 = 0

2y-4x +5 = 0

We need to find the intersection points.

First, we will rewrite the equations as functions of x.

==> y= -x + 2 ...............(1)

==> y= (4x-5)/2 =

==> y= 2x - 5/2..............(2)

Now we will determine the point of intersection when y= y

==> -x + 2 = 2x - 5/2

==> -3x = -5/2 -2

==> -3x = -9/2

We will divide by -3.

==> x = 3/2

==> y= -x +2 = -3/2 +2 = 1/2

==> y= 1/2

**Then, the intersection point is ( 3/2, 1/2)**

To find the point of intersection of the lines y+x -2 = 0 and 2y-4x +5 = 0.

y+x-2 = 0...(1) and 2y-4x+5 = 0...(2).

2*(1)-(2) gives 2(y+x-2) -(2y-4x+5) = 0

=> 2x-4+4x-5 = 0

=>6x - 9 = 0. So 6x= 9. Or **x**= -9/6 = **3/2**

We put x= 3/2 in (1): y+x-2 = 0. y+3/2-2 = 0. So **y **= -3/2+2 = **1/2**.

Therefore x = 3/2 and y = 1/2 . So the point od itersection of the lines is (x,y) = (3/2 , 1/2).