Question

Which of these correctly explains the solution of the system of equations shown
below?
2x + 3y = 6
x+ 3y = 12
O A The equations have x-intercepts at 3 and 12; therefore, (3, 12) is the
O
B. The values of x= -6 and y= 6 satisfy both the equations; therefore, (-6, 6) is
the solution.
O
C. The lines representing the equations intersect at x= 1 and y = o; therefore,
(1, 0) is the solution.
The equations have v-intercents at 2 and 4: therefore
the solution

Answer 1

The solution of the system of equations is the point (-6, 6), so the correct option is B.

Which statements are correct about the system of equations?

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:

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