Question

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

Answer 1

B. One

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).