21.8k views
4 votes
Use the elimination method to solve the system of equations.

2x + 3y = 18
3x - 3y = 12
O A. (6,10)
OB. (2,6)
O C. (2,4)
OD. (6,2)

User Informat
by
8.3k points

1 Answer

1 vote
To use the elimination method to solve the given system of equations:

2x + 3y = 18
3x - 3y = 12

First, add the two equations together to eliminate the y variable:

(2x + 3y) + (3x - 3y) = 18 + 12

The y variables cancel each other out:

2x + 3x = 30

Combine the x terms:

5x = 30

Now, solve for x by dividing both sides by 5:

5x / 5 = 30 / 5

x = 6

Next, substitute the value of x back into either of the original equations to solve for y. We'll use the first equation:

2x + 3y = 18
2(6) + 3y = 18
12 + 3y = 18

Subtract 12 from both sides:

3y = 6

Now, divide both sides by 3 to solve for y:

3y / 3 = 6 / 3

y = 2

The solution to the system of equations is (x, y) = (6, 2), which corresponds to option D.
User Paolo Ardissone
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.