Solve the system of equations by the elimination method.
-$\begin{array} { l }
\frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 21 \
\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 7
\end{array}$
A) $( - 12,9 )$
B) $( 12,9 )$
C) $( 9 , - 12 )$
D) $( - 12 , - 9 )$

Question

Solve the system of equations by the elimination method.
-$\begin{array} { l } 
\frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 21 \
\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 7
\end{array}$
A) $( - 12,9 )$
B) $( 12,9 )$
C) $( 9 , - 12 )$
D) $( - 12 , - 9 )$

Quizplus · Accepted Answer

To solve the system of equations by the elimination method, first, we need to make the coefficients of either $x$ or $y$ the same in both equations. Let's choose to equalize the coefficients of $x$.The first equation is $\frac{3}{2}x - \frac{1}{3}y = -21$, and the second equation is $\frac{3}{4}x + \frac{2}{9}y = -7$.To equalize the coefficients of $x$, we can multiply the entire second equation by 2, resulting in $\frac{3}{2}x + \frac{4}{9}y = -14$.Now, we have:1. $\frac{3}{2}x - \frac{1}{3}y = -21$2. $\frac{3}{2}x + \frac{4}{9}y = -14$Subtract the second equation from the first to eliminate $x$:$-\frac{1}{3}y - \frac{4}{9}y = -21 + 14$Combining the $y$ terms gives us:$-\frac{3}{9}y - \frac{4}{9}y = -7$$-\frac{7}{9}y = -7$Solving for $y$ gives:$y = -7 \times \frac{-9}{7} = 9$Now, substitute $y = 9$ into one of the original equations to solve for $x$. Using the first equation:$\frac{3}{2}x - \frac{1}{3}(9) = -21$$\frac{3}{2}x - 3 = -21$$\frac{3}{2}x = -18$$x = -18 \times \frac{2}{3} = -12$Therefore, the solution to the system of equations is $x = -12$ and $y = 9$, which corresponds to choice A $(-12, 9)$.

Solve the System of Equations by the Elimination Method 32x−13y=−2134x+29y=−7\begin{array} { l } \frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 21 \\\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 7\end{array}23​x−31​y=−2143​x+92​y=−7​

Solve the System of Equations by the Elimination Method $\begin{array} { l } \frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 21 \\\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 7\end{array}$