Solve the system of equations and choose the correct ordered pair.

3x + 2y = 12

6x + 3y = 21

A(4, 3)
B(4, 0)
C(2, 3)
D(3, 2)

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Verified Answer :

Anonymous Anonymous · Answer 1 · 2016-12-11T09:40:24-05:00

I hope this helps you

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pemanuel pemanuel · Answer 2 · 2019-09-23T12:44:25-04:00

Answer:

C.

Step-by-step explanation:

We are going to solve it with substitution, that is, we are going to clear one variable and then replace it in the other equation. Then,

\(3x + 2y = 12\)

\(3x = 12-2y\)

\(x = \frac{12-2y}{3}\)

\(x = \frac{12}{3}-\frac{2y}{3}\)

\(x = 4-\frac{2y}{3}.\)

Now, we replace that x value in the equation 6x + 3y = 21:

\(6(4-\frac{2y}{3}) + 3y = 21\)

\(24-\frac{12y}{3} + 3y = 21\)

\(24-4y + 3y = 21\)

\(24-y = 21\)

\(-y = 21-24\)

\(-y = -3\)

\(y = 3.\)

Finally, we replace the y value found to find x.

\(x = 4-\frac{2*3}{3}\)

\(x = 4-2\)

\(x = 2.\)

So, the solution is (x,y)=(2,3). Then, the answer is C.