Solve the system by the addition method.
-$$\begin{array} { l }
- 2 x - 5 y = - 17 \
5 x - 3 y = - 4
\end{array}$$
A) $\{ ( 1,3 ) \}$
B) $\{ ( - 1 , - 3 ) \}$
C) $\{ ( 1 , - 3 ) \}$
D) $\{ ( - 1,3 ) \}$

Question

Solve the system by the addition method.
-$$\begin{array} { l } 
- 2 x - 5 y = - 17 \
5 x - 3 y = - 4
\end{array}$$
A) $\{ ( 1,3 ) \}$
B) $\{ ( - 1 , - 3 ) \}$
C) $\{ ( 1 , - 3 ) \}$
D) $\{ ( - 1,3 ) \}$

Quizplus · Accepted Answer

To solve the system by the addition method, we first aim to eliminate one of the variables by adding the equations together. To do this, we can multiply the first equation by 5 and the second equation by 2 to get the coefficients of $x$ to be opposites:$$5(-2x - 5y) = 5(-17)$$$$2(5x - 3y) = 2(-4)$$This simplifies to:$$-10x - 25y = -85$$$$10x - 6y = -8$$Adding these equations together to eliminate $x$:$$-10x + 10x - 25y - 6y = -85 - 8$$$$-31y = -93$$Solving for $y$, we get:$$y = \frac{-93}{-31} = 3$$To find $x$, substitute $y = 3$ into one of the original equations, for example, the first one:$$-2x - 5(3) = -17$$$$-2x - 15 = -17$$$$-2x = -2$$$$x = 1$$Therefore, the solution is $(1, 3)$, which corresponds to choice A.

Solve the System by the Addition Method −2x−5y=−175x−3y=−4\begin{array} { l } - 2 x - 5 y = - 17 \\5 x - 3 y = - 4\end{array}−2x−5y=−175x−3y=−4​

Solve the System by the Addition Method $\begin{array} { l } - 2 x - 5 y = - 17 \\5 x - 3 y = - 4\end{array}$