Find the point of intersection between the lines 2y=-4x+4 and 3y=10x-3

The easiest way to find the point of intersection between two lines is to use simultaneous equations. Begin by setting y=y or x=x. In this case we will be setting y=y, in order to do this you must manipulate the equations such that the multiplier of both of the y values is the same.
We will begin by multiplying the first equation (2y=-4x+4) by 3 which gives us
6y=-12x+12
We then multiply the second equation (3y=10x-3) by 2 which gives us
6y=20x-6
now we can set these equations equal to each other because at the point of intersection the y value of each line will be the same, therefore since y=y, 6y=6y and it then follows
-12x+12=20x-6
We can then solve this equation for
x=1/2
now that we know the x value at the point of intersection we simply choose one of the equations (preferably the simplest) and input the x value we found into that equation, this will then give us our y value.
3y=10x-3
3y=5-3
y=2/3
Thus the point of intersection is (1/2, 2/3)