Question

Use the elimination method to solve the system of equations. Choose the correct ordered pair.

a) (−2,11)
b) (2,3)
c) (3,2)
d) (−3,−2)

Answer 1

The correct ordered pair obtained by using the elimination method to solve the system of equations is (3,2) thus option C is correct.

Step-by-step explanation:

To solve the system of equations using the elimination method, we eliminate one of the variables by adding or subtracting the equations. Let's consider the system of equations:

`\[ \begin{cases} 2x + 3y = 12 \\ 4x - y = 6 \end{cases} \]`

To eliminate one of the variables, we can multiply the second equation by 3 to make the coefficients of (y) in both equations the same:

`\[ \begin{cases} 2x + 3y = 12 \\ 12x - 3y = 18 \end{cases} \]`

Now, we can add the two equations to eliminate (y):

14x = 30

Solving for (x), we get
`\(x = (15)/(7)\)`. Substituting this value back into one of the original equations, let's use the first equation:

`\[ 2 \left( (15)/(7) \right) + 3y = 12 \]`

Solving for (y), we get
`\(y = (6)/(7)\).` Therefore, the solution to the system of equations is
`\( (x, y) = \left( (15)/(7), (6)/(7) \right) \),` which simplifies to (3,2) thus option C is correct.