What is the point of intersection of 4x+ 3y =0 and 7x + 5y +1 =0

Let d1 and d2 be two lines such
that:

d1 : 4x + 3y =0

d2: 7x +
5y + 1 = 0

Both lines are intersecting at one point , then
the point of intersection sould verify both equations. Therefore te point is a common
solution for the system.

Then we need to solve the
system:

Let us use the elemination
method:

Multiply (1) by -5 and multiply (2) by
3:

-20x - 15 y =
0.........(1)

21x + 15x = -3
..........(2)

==> x =
-3

Now to find y, we will substitue with
(1):

4x + 3y = 0

==> y=
(-4/3)*x = -4/3 * -3 = 4

==> y=
4

Then both lines intersects
at the point (-3, 4)