Question

PLS HELP

Graph the following system of equations. After graphing state what is the solution for this system.

2x + 6y = 12
4x + 12y = 36

Answer 1

The system of equations, 2x + 6y = 12 and 4x + 12y = 36, represents parallel lines with the same slope but different y-intercepts. As a result, the system has no solution, indicating an inconsistent system.

To graph the system of equations, let's first rearrange each equation into slope-intercept form (y = mx + b) to identify their slopes (m) and y-intercepts (b).

**Equation 1:**

2x + 6y = 12

6y = -2x + 12

`\[y = -(1)/(3)x + 2\]`

**Equation 2:**

4x + 12y = 36

12y = -4x + 36

`\[y = -(1)/(3)x + 3\]`

Now we can graph these lines:

- The slope for both lines is
`\(-(1)/(3)\)`, indicating they are parallel.

- The y-intercept for the first line is 2, and for the second line is 3.

Since the slopes are equal and the y-intercepts are different, the lines are parallel and have no intersection. Therefore, there is no solution to the system of equations. The system is inconsistent and represents parallel lines that do not intersect.