The linear combination method is applied to a system of equations as shown.

Question

4(.25x + .5y = 3.75) → x + 2y = 15
One-fourth(4x – 8y = 12) → x – 2y = 3
2x = 18
What is the solution of the system of equations?

(1,2)
(3,9)
(5,5)
(9,3)

Answer 1

Let's analyze the system of equations given in the problem:

From the linear combination method applied here, we have two equations stated after simplification:

1. \( x + 2y = 15 \) (from \( 4(0.25x + 0.5y = 3.75) \))
2. \( x - 2y = 3 \) (from \( \frac{1}{4}(4x - 8y = 12) \))

To find the solution for the system of equations, we can solve these two equations simultaneously.

1. Start with the first equation:

   \[ x + 2y = 15 \quad (1) \]

2. Solve the second equation for \( x \):

   \[ x - 2y = 3 \quad (2) \] Rearranging gives: \[ x = 2y + 3 \quad (3) \]

3. Substitute equation (3) into equation (1):

   \[ (2y + 3) + 2y = 15 \]

   Combining like terms:

   \[ 4y + 3 = 15 \]

   Subtracting 3 from both sides:

   \[ 4y = 12 \]

   Dividing both sides by 4:

   \[ y = 3 \]

4. Substitute \( y = 3 \) back into equation (3) to find \( x \):

   \[ x = 2(3) + 3 \] \[ x = 6 + 3 = 9 \]

Thus, the solution to the system of equations is:

\[ (x, y) = (9, 3) \]

Therefore, the correct answer from the options provided is:

(9, 3)