How many times do the lines intersect? *
Y= - 4x +1
Y=7x + 2
​

Once.  The point of intersection is (-5/7, 3)

Step-by-step explanation:

Once.  You have two straight lines here with different slopes, and neither is the negative reciprocal of the other.  There is one solution to this system of linear equations.

Setting the two equations equal to each other, we get

y = -4 + 1 = 7x + 2, or

-3 = 7x + 2, or

7x = -5, or x = -5/7.  

From the first equation and x = -5/7, we find y:

y = 7(-5/7) + 2, or y = -5 + 2, or y = 3.

The ONE solution is (-5/7, 3)