How many solutions does this system of equations have ??

y= 4x + 3 and 2y - 8x =3

2 (4x+3) - 8 x = 3

8 x + 6 - 8 x = 3
0 x = - 3

oh my, division by zero
try
y = 4x + 3
and
y = 4x + 3/2
ah, we have a problem here
two parallel lines, same slope
but different y axis intercepts
They never touch each other, ever/
NO SOLUTION

Thanks @damon.

You are welcome.

To determine the number of solutions for a system of equations, you need to solve the system and analyze the solutions.

Let's solve the system of equations by using the method of substitution:

First, substitute the expression for y from the first equation into the second equation:

2y - 8x = 3
2(4x + 3) - 8x = 3
8x + 6 - 8x = 3

Simplifying the equation further:

6 = 3

Now, notice that this equation is not true. There is a contradiction, which means that the system of equations is inconsistent, and there are no solutions.

Therefore, the given system of equations has no solutions.