Where do the lines 2y = 4x + 2 and - 3x + y = 4 intersect?

Rearrange the second equation in the form y = mx + c to get y = 3x + 4. Divide the first equation by 2 to get y = 2x + 1. When the lines intersect, they'll have the same x and y values, hence, set the equations equal to each other to find the x co-ordinate: 2x + 1 = 3x + 4. Collecting like terms gives 1 = x + 4, and then taking the 4 to the other side of the equation gives x = -3. This value is substituted into either equation, allowing you to find the y co-ordinate: (using equation 1) y = 2(-3) + 1, which gives y = -5. Therefore, the two lines intersect at the point (-3,-5).