What is the point of intersection of 3x + 19y =7 and x + 2y = 1

To find the point ofintersection of the
lines:

3x+19y = 7 and

x+2y =
1.

The cooordinates of any point on a line should satisfy
the equation of the line. Therefore the coordintes of point of intersection of the lines
should satisfy both the llines. In other words, if we solve equation simultaneously, the
solution is the coodintes of the intersection point of the given
lines:

We solve by substitution
method.

3+19y = 7. Therefore 3x = 7-19y. So , x =
(7-19y)/3. We substitute  x= (7-19y)/3 in the other equation x+2y =
1.

(7-19y)/3+2y = 1.

Multiply
by 3 :

7-19y+6y = 3

7 -13y =
3.

-13y = 3-7 = -4.

y = =
-4/-13 = 4/13.

Substitute  y = 4/13 in 3x+19y = 7:
3x+19(4/13) = 7 :

3x = 7-19(4/13) =
15/13

x = (15/13)/3 =
5/13

Therefore x = 5/13  and y =
4/13.

Therefore the point of intersection is P whose
coordinates are (5/13 , 4/13).