solve the following two equations algebraically.

4x+3y=12
4x-y=4

give the coordinates of intersection.

Subtract the second equation from the first. That will leave you with

4y = 8
Now solve for y. Once you have that, use either of your equations to get x.

To solve this system of equations algebraically, we can use the method of substitution or elimination. Let's use the method of elimination.

First, let's multiply the second equation by 3 so that the coefficients of the "y" terms in both equations will cancel when we add them together:

Original equations:
1) 4x + 3y = 12
2) 4x - y = 4

Multiply equation (2) by 3:
3) 12x - 3y = 12

Now, add equation (1) and equation (3) together to eliminate the "y" terms:
4) (4x + 3y) + (12x - 3y) = 12 + 12
16x = 24

Divide both sides of equation (4) by 16 to solve for x:
5) x = 24/16
x = 3/2

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use equation (1):

6) 4x + 3y = 12
(4 * 3/2) + 3y = 12
6 + 3y = 12
3y = 12 - 6
3y = 6
y = 6/3
y = 2

So, the solution to the system of equations is x = 3/2 and y = 2. Therefore, the coordinates of the intersection are (3/2, 2).