Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically. $$\left\{ \begin{array} { l }
3 x + 11 y = 12 \
- 2 x - 5 y = 6
\end{array} \right.$$
A)(18,6)
B)(-18,-6)
C)(-18,18)
D)(-18,6)
E)(18,-6)

Question

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ $$\left\{ \begin{array} { l } 
3 x + 11 y = 12 \
- 2 x - 5 y = 6
\end{array} \right.$$ ​
A)​(18,6)
B)(-18,-6) ​
C)(-18,18)
D)(-18,6)
E)​(18,-6) ​

Quizplus · Accepted Answer

To solve the system of equations by elimination, we aim to eliminate one variable by adding or subtracting the equations. First, we can multiply the first equation by 2 and the second equation by 3 to get the coefficients of $x$ to be opposites:$$6x + 22y = 24$$$$-6x - 15y = 18$$Adding these equations together eliminates $x$, resulting in:$$7y = 42$$Solving for $y$ gives:$$y = 6$$Substitute $y = 6$ into one of the original equations to solve for $x$. Using the first equation:$$3x + 11(6) = 12$$$$3x + 66 = 12$$$$3x = -54$$$$x = -18$$Therefore, the solution is $(x, y) = (-18, 6)$, which corresponds to choice D.

Solve the System of Linear Equations by the Method of Elimination.Find