Question

What is the value of y in the solution to the system of equations? 1/3x + 1/4y = 1 2x-3y=-30​

Answer 1

Answer:

y = 8

Step-by-step explanation:

$\left\{\begin{array}{ccc}\dfrac{1}{3}x+\dfrac{1}{4}y=1&\text{multiply both sides by 12}\\2x-3y=-30\end{array}\right\\\left\{\begin{array}{ccc}12\!\!\!\!\!\diagup^4\cdot\dfrac{1}{3\!\!\!\!\diagup_1}x+12\!\!\!\!\!\diagup^3\cdot\dfrac{1}{4\!\!\!\!\diagup_1}y=12\cdot1\\2x-3y=-30\end{array}\right\\\left\{\begin{array}{ccc}4x+3y=12\\2x-3y=-30&\text{multiply both sides by (-2)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}4x+3y=12\\-4x+6y=60\end{array}\right}\qquad\text{add both sides of the equations}$

$.\qquad9y=72\qquad\text{divide both sides by 9}\\.\qquad y=8$