# Determine the common point of the lines 2x+y-5=0 and -3x+4y-9=0.

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Common point of two equations means that the point is the intersection of two lines, that means both lines should verify the point.

2x+y-5 =0

==> y = -2x+5

-3x+4y-9 = 0

==> y = (3/4)x +9/4

then -2x + 5 = (3/4)x +9/4

==> 5-9/4 = (11/4)x

==> x = 4/11 (11/4) = 1

then y = -2(1)+5 = 3

then both lines intersect at the point (1,3)

To determine the crossing point of the 2 lines, we have to solve the system formed from their equations:

2x+y=5 (1)

-3x+4y=9 (2)

We'll multiply the relation (1) by 3 and the relation (2), by 2, and after that, we'll add (1) to (2). We'll obtain:

6x+3y-6x+8y = 15 + 18

After reducing similar terms, we'll get:

11y = 33

y = 33/11

**y=3**

We'll substitute y by 3, into the relation (1):

2x+3 = 5

2x = 5-3

2x = 2

**x = 1**

**The crossing point is A (1,3).**

The common pointsof the lines 2x+y-5= 0........(1) and -3x+4y-0 = 0..........(2) are got by solving the two simultaneous equations.

From (1), y = 5-2x. Substotuting this in eq(2), we get:

-3x+4(5-2x)-9 = 0. Or

-3x+20-8x-9 = 0. Or

-3x-8x+11 = 0. Or -11x= -11. Or x = 1

Substituting x = 1 in eq(1) we get:

2(1)+y -5 = 0. Or y = 5-2 = 3