Question

the linear combination method is applied to a system of equations as shown.
$4(0.25x + 5y = 3.75) \to x + 2y = 15$
$\frac{1}{4}(4x - 8y = 12) \to x - 2y = 3$
$2x = 18$
what is the solution of the system of equations?
\bigcirc (1,2)
\bigcirc (3,9)
\bigcirc (5,5)
\bigcirc (9,3)

Explanation:

Step1: Solve for $x$

$2x = 18$
$x = \frac{18}{2} = 9$

Step2: Substitute $x=9$ into $x-2y=3$

$9 - 2y = 3$
$-2y = 3 - 9 = -6$
$y = \frac{-6}{-2} = 3$

Step3: Verify with $x+2y=15$

$9 + 2(3) = 9 + 6 = 15$, which holds true.

Answer:

(9,3)