(25 Points) Please help! The graph of this system of equations is which of the following?

2x + y = 6
6x + 3y = 12

Overlapping lines
Parallel lines
Intersecting lines
A curve intersecting with a line

The lines are parallel.

Step-by-step explanation:

2x + y = 6

Convert to the slope-intercept form y = mx + b:

2x + y = 6          subtract 2x from both sides

y = -2x + 6

for x = 0 → y = -2(0) + 6 = 0 + 6 = 6 → (0, 6)

for x = 3 → y = -2(3) + 6 = -6 + 6 = 0 → (3, 0)

6x + 3y = 12

Convert to the slope-intercept form:

6x + 3y = 12            subtract 6x from both sides

3y = -6x + 12          divide both sides by 3

y = -2x + 4

for x = 0 → y= -2(0) + 4 = 0 + 4 = 4 → (0, 4)

for x = 2 → y = -2(2) + 4 = -4 + 4 = 0 → (2, 0)

hope this helps

x = 12

y = 1

for the points!