Use the elimination-by-addition method to solve the system. $$\left( \begin{array} { c }
4 x - 6 y = 10 \
4 x + 2 y = - 14
\end{array} \right)$$
A) ( -2, 3)
B) ( 2, 3)
C) ( -2, -3)
D) infinitely many solutions
E) no solutions

Question

Use the elimination-by-addition method to solve the system. $$\left( \begin{array} { c } 
4 x - 6 y = 10 \
4 x + 2 y = - 14
\end{array} \right)$$
A) ( -2, 3)
B) ( 2, 3)
C) ( -2, -3)
D) infinitely many solutions
E) no solutions

Quizplus · Accepted Answer

If we add the two equations together, the $4x$ terms will cancel out, leaving us with $-4y=-4.$ Dividing by $-4$ gives us $y=1.$ Plugging this value of $y$ into either of the original equations, we get $4x-6=10$ or $4x+2=-14.$ Solving for $x$ in each case gives us $x=-2$ in both cases. Therefore, the solution is $(x,y)=(-2,1).$ This corresponds to choice C.

Use the Elimination-By-Addition Method to Solve the System (4x−6y=104x+2y=−14)\left( \begin{array} { c } 4 x - 6 y = 10 \\4 x + 2 y = - 14\end{array} \right)(4x−6y=104x+2y=−14​)

Use the Elimination-By-Addition Method to Solve the System $\left( \begin{array} { c } 4 x - 6 y = 10 \\4 x + 2 y = - 14\end{array} \right)$