Solve the system using the elimination-by-addition method. $$\left( \begin{array} { c }
4 x + y = 22 \
8 x - 2 y = 20
\end{array} \right)$$
A) ( 13, 15 )
B) ( 4, 6 )
C) ( 16, 18 )
D) ( 8, 10 )
E) ( 0, 2 )

Question

Solve the system using the elimination-by-addition method. $$\left( \begin{array} { c } 
4 x + y = 22 \
8 x - 2 y = 20
\end{array} \right)$$
A) ( 13, 15 )
B) ( 4, 6 )
C) ( 16, 18 )
D) ( 8, 10 )
E) ( 0, 2 )

Quizplus · Accepted Answer

To solve the system using the elimination-by-addition method, we first align the equations and then manipulate them to eliminate one variable. The given system is:$$4x + y = 22$$$$8x - 2y = 20$$To eliminate $y$, we can multiply the first equation by 2 to get:$$8x + 2y = 44$$Now, adding this to the second equation:$$8x - 2y = 20$$$$+$$$$8x + 2y = 44$$$$=$$$$16x = 64$$Solving for $x$, we get:$$x = 64 / 16 = 4$$Substitute $x = 4$ into the first equation to solve for $y$:$$4(4) + y = 22$$$$16 + y = 22$$$$y = 22 - 16 = 6$$Therefore, the solution is $x = 4$, $y = 6$, which corresponds to choice (B).

Solve the System Using the Elimination-By-Addition Method (4x+y=228x−2y=20)\left( \begin{array} { c } 4 x + y = 22 \\8 x - 2 y = 20\end{array} \right)(4x+y=228x−2y=20​)

Solve the System Using the Elimination-By-Addition Method $\left( \begin{array} { c } 4 x + y = 22 \\8 x - 2 y = 20\end{array} \right)$