Solve the system using the elimination-by-addition method. $$\left( \begin{array} { c }
5 x + 3 y = 19 \
2 x - 4 y = - 8
\end{array} \right)$$
A) ( 4, 5 )
B) ( 17, 18 )
C) ( 5, 6 )
D) ( 14, 15 )
E) ( 2, 3 )

Question

Solve the system using the elimination-by-addition method. $$\left( \begin{array} { c } 
5 x + 3 y = 19 \
2 x - 4 y = - 8
\end{array} \right)$$
A) ( 4, 5 )
B) ( 17, 18 )
C) ( 5, 6 )
D) ( 14, 15 )
E) ( 2, 3 )

Quizplus · Accepted Answer

To solve the system using the elimination-by-addition method, we first aim to eliminate one of the variables by adding the two equations. To do this efficiently, we can manipulate the equations to have coefficients for $y$ that are opposites. Given equations:1. $5x + 3y = 19$2. $2x - 4y = -8$We can multiply the first equation by 4 and the second equation by 3 to get the coefficients of $y$ to be 12 and -12, respectively:1. $20x + 12y = 76$2. $6x - 12y = -24$Adding these equations together to eliminate $y$, we get:$$26x = 52$$Solving for $x$, we find:$$x = 2$$To find $y$, we can substitute $x = 2$ back into one of the original equations. Using the first equation:$$5(2) + 3y = 19$$$$10 + 3y = 19$$$$3y = 9$$$$y = 3$$Therefore, the solution to the system is $x = 2$, $y = 3$, which corresponds to choice E.

Solve the System Using the Elimination-By-Addition Method (5x+3y=192x−4y=−8)\left( \begin{array} { c } 5 x + 3 y = 19 \\2 x - 4 y = - 8\end{array} \right)(5x+3y=192x−4y=−8​)

Solve the System Using the Elimination-By-Addition Method $\left( \begin{array} { c } 5 x + 3 y = 19 \\2 x - 4 y = - 8\end{array} \right)$