Solve the system of equations by the elimination method.
-$$\left\{ \begin{array} { l }
- 3 x - 7 y = - 26 \
- 5 x + 4 y = 35
\end{array} \right.$$
A) $( - 3,5 )$
B) $( 3 , - 5 )$
C) $( 3,5 )$
D) $( - 3 , - 5 )$

Question

Solve the system of equations by the elimination method.
-$$\left\{ \begin{array} { l } 
- 3 x - 7 y = - 26 \
- 5 x + 4 y = 35
\end{array} \right.$$
A) $( - 3,5 )$
B) $( 3 , - 5 )$
C) $( 3,5 )$
D) $( - 3 , - 5 )$

Quizplus · Accepted Answer

To solve the system by elimination, we aim to eliminate one variable by adding or subtracting the equations. First, we can multiply the first equation by 4 and the second by 7 to get the coefficients of $y$ to be the same (with opposite signs):$$4(-3x - 7y) = 4(-26) \rightarrow -12x - 28y = -104$$$$7(-5x + 4y) = 7(35) \rightarrow -35x + 28y = 245$$Adding these equations together to eliminate $y$:$$-12x - 28y - 35x + 28y = -104 + 245$$$$-47x = 141$$$$x = 141 / -47$$$$x = -3$$Substitute $x = -3$ into one of the original equations to solve for $y$. Using the first equation:$$-3(-3) - 7y = -26$$$$9 - 7y = -26$$$$-7y = -26 - 9$$$$-7y = -35$$$$y = 5$$Therefore, the solution is $(-3, 5)$.

Solve the System of Equations by the Elimination Method {−3x−7y=−26−5x+4y=35\left\{ \begin{array} { l } - 3 x - 7 y = - 26 \\- 5 x + 4 y = 35\end{array} \right.{−3x−7y=−26−5x+4y=35​

Solve the System of Equations by the Elimination Method $\left\{ \begin{array} { l } - 3 x - 7 y = - 26 \\- 5 x + 4 y = 35\end{array} \right.$