The solution of the system of equations is the point (-6, 6), so the correct option is B.
<h3>
Which statements are correct about the system of equations?</h3>
Here we have the system of equations:
2x + 3y = 6
x + 3y = 12
First, let's write these two lines in the slope-intercept form:
y = (6 - 2x)/3 = 2 - (2/3)*x
y = (12 - x)/3 = 4 - (1/3)*x
Now, because "y" is the represents the same variable in both equations, we can write:
2 - (2/3)*x = y = 4 - (1/3)*x
Now we can solve that for x.
2 - (2/3)*x = 4 - (1/3)*x
2 - 4 = (2/3)*x - (1/3)*x
-2 = (1/3)*x
3*(-2) = x = -6
Now, to get the y-value of the solution we can evaluate any of the two lines in x = -6, evaluating the first we get:
y = 4 - (1/3)*x = 4 - (1/3)*(-6) = 4 + 2 = 6
Then the solution of the system is the point (-6, 6). Then the correct statement is B:
"The values of x= -6 and y= 6 satisfy both the equations; therefore, (-6, 6) is the solution."
If you want to learn more about systems of equations:
brainly.com/question/13729904
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