Question

the equations were multiplied by constants and added together to determine that the value of x in the system of equations is -3?\\
\\(\frac{1}{2}x - \frac{1}{3}y = -1\\)\\
\\(-\frac{3}{4}x + \frac{1}{3}y = 12\\)\\
what is the value of y?\\
\\(\circ -15\\)\\
\\(\circ 9\\)\\
\\(\circ -9\\)\\
\\(\circ 15\\)

Explanation:

Step1: Substitute x=-20 into first equation

Substitute $x=-20$ into $\frac{1}{2}x - \frac{1}{3}y = -1$:
$\frac{1}{2}(-20) - \frac{1}{3}y = -1$

Step2: Simplify the constant term

Calculate $\frac{1}{2}(-20)$:
$-10 - \frac{1}{3}y = -1$

Step3: Isolate the y-term

Add 10 to both sides:
$-\frac{1}{3}y = -1 + 10$
$-\frac{1}{3}y = 9$

Step4: Solve for y

Multiply both sides by -3:
$y = 9 \times (-3)$

Answer:

$-27$

(Note: -27 is not listed in the provided options, but this is the mathematically correct solution from the given system and x-value.)