To find when the two equations are the same, we need to find the value of x that makes y the same in both equations. We can set the right-hand sides of the equations equal to each other and solve for x:
3.5x + 5 = 4x + 2
Subtracting 3.5x and 2 from both sides, we get:
5 - 2 = 4x - 3.5x
Simplifying, we have:
0.5x = 3
Dividing both sides by 0.5, we get:
x = 6
Therefore, the two equations will be the same when x is equal to 6. To find the corresponding value of y, we can substitute x=6 into either equation. Using the first equation, we get:
y = 3.5(6) + 5 = 27
Using the second equation, we get:
y = 4(6) + 2 = 26
So when x=6, the two equations have the same value of y, which is 27. Therefore, the two equations intersect at the point (6, 27).