Solve the following system of linear equation by using graphs? 2x+3y=-6 2x+y=2?

To solve the system of linear equations by using graphs, we need to graph each equation and find the point of intersection.

First, let's graph the equation 2x + 3y = -6:

To graph this equation, we can rearrange it to solve for y:
3y = -2x - 6
y = (-2/3)x - 2

Now, let's graph the equation 2x + y = 2:

To graph this equation, we can rearrange it to solve for y:
y = -2x + 2

Now, we can plot the two lines on the same graph:

The first equation, y = (-2/3)x - 2, has a y-intercept of -2 and a slope of -2/3. We can plot two points on this line, such as (0, -2) and (3, -4).

The second equation, y = -2x + 2, has a y-intercept of 2 and a slope of -2. We can plot two points on this line, such as (0, 2) and (1, 0).

Now, we can see that the two lines intersect at the point (3, -4). Therefore, the solution to the system of linear equations is x = 3 and y = -4.