Use the echelon method to solve the system.
-$$
\begin{array}{l}
\frac{3 x}{2}-\frac{y}{3}=-18 \
\frac{3 x}{4}+\frac{2 y}{9}=-9
\end{array}
$$
A) $ (0,-12) $
B) $ (-12,0) $
C) $ (12,0) $
D) $ (0,12) $

Question

Quizplus · Accepted Answer

To solve the system using the echelon method, we first need to manipulate the equations to make them easier to work with. We can multiply each equation by a common denominator to eliminate the fractions. For the first equation, multiplying by 6 gives us $9x - 2y = -108$, and for the second equation, multiplying by 36 gives us $27x + 8y = -324$. Now, we can use the elimination method to solve for $x$ and $y$.Multiplying the first equation by 4 gives us $36x - 8y = -432$, and adding this to the second equation (which is $27x + 8y = -324$) eliminates $y$, giving us $63x = -756$. Solving for $x$ gives $x = -12$.Substituting $x = -12$ into one of the original equations (easier to use the first one after clearing fractions: $9x - 2y = -108$) gives us $9(-12) - 2y = -108$, which simplifies to $-108 - 2y = -108$. Solving for $y$ gives $y = 0$.Therefore, the solution to the system is $x = -12$, $y = 0$, which corresponds to choice B.

Use the Echelon Method to Solve the System 3x2−y3=−183x4+2y9=−9\begin{array}{l}\frac{3 x}{2}-\frac{y}{3}=-18 \\\frac{3 x}{4}+\frac{2 y}{9}=-9\end{array}23x​−3y​=−1843x​+92y​=−9​

Use the Echelon Method to Solve the System $\begin{array}{l}\frac{3 x}{2}-\frac{y}{3}=-18 \\\frac{3 x}{4}+\frac{2 y}{9}=-9\end{array}$