Where do the lines 3x + 19y =7 and x + 2y = 1 meet?

3x + 19y =
7................(1)

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

We need to determine the
intersection points of the lines (1) and (2).

The points of
intersection are the points that verifies both equations. Then the points of
intersections are the solution of the system.

Let us solve
the system.

We will re-write equation
(2).

x+ 2y = 1

==> x=
1- 2y

Now we will use the substitution method to
solve.

Let us substitute with x= 1- 2y into
(1).

3x + 19 y = 7

==>
3( 1- 2y) + 19y = 7

==> 3 - 6y + 19 y =
7

==> 3 + 13y =
7

==> 13y =
4

==> y=
4/13

==> x= 1- 2y = 1- 2*4/13 = 1- 8/13 =
5/13

==> x =
5/13

Then, the lines intersects at the point
( 5/13, 4/13)