How many solutions does the following system of equations have? 2y= 5x+4
y= 3x+2
Α. Two
B. One
C. Zero
D. Infinitely many

  B.  One

Step-by-step explanation:

The lines have different slopes, so they must intersect at exactly one point.

There is One solution to this system.

_____

If you solve the first equation for y, you get ...

  y = (5/2)x +2

This has a different slope (x-coefficient) than the second equation does, but it has the same y-intercept. That y-intercept is the point of intersection of the lines, hence the solution: (x, y) = (0, 2).

b. 2

step-by-step explanation:

the slope of a line =δy/δx

δy= y₂-y₁

δx= x₂-x₁

therefore, using the points (-2,-3)   and (3,7) we can calculate gradient as follows:

m=(7--3)/(3--2) (a number minus a negative number the sign changes to a plus)

m=(7+10)/(3+2)

=10/5

=2