Use the elimination-by-addition method to solve the system. $$\left( \begin{array} { c }
6 x + 5 y = - 14 \
5 x - 7 y = 33
\end{array} \right)$$
A) ( 1, -4)
B) ( 4, 1)
C) ( 4, -1)
D) infinitely many solutions
E) no solutions

Question

Use the elimination-by-addition method to solve the system. $$\left( \begin{array} { c } 
6 x + 5 y = - 14 \
5 x - 7 y = 33
\end{array} \right)$$
A) ( 1, -4)
B) ( 4, 1)
C) ( 4, -1)
D) infinitely many solutions
E) no solutions

Quizplus · Accepted Answer

To solve the system using elimination-by-addition, we first multiply the equations to align the coefficients of one of the variables. Multiply the first equation by 7 and the second by 5 to eliminate y:  $$ 42x + 35y = -98 $$  $$ 25x - 35y = 165 $$  Add the equations:  $$ 67x = 67 $$  $$ x = 1 $$  Substitute $ x = 1 $ into the first equation:  $$ 6(1) + 5y = -14 $$  $$ 6 + 5y = -14 $$  $$ 5y = -20 $$  $$ y = -4 $$  Thus, the solution is (1, -4).

Use the Elimination-By-Addition Method to Solve the System (6x+5y=−145x−7y=33)\left( \begin{array} { c } 6 x + 5 y = - 14 \\5 x - 7 y = 33\end{array} \right)(6x+5y=−145x−7y=33​)

Use the Elimination-By-Addition Method to Solve the System $\left( \begin{array} { c } 6 x + 5 y = - 14 \\5 x - 7 y = 33\end{array} \right)$